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Threshold reweighted Nadaraya–Watson estimation of jump-diffusion models Probab. Uncertain. Quant. Risk Pub Date : 2022-01-01 Kunyang Song,Yuping Song,Hanchao Wang
In this paper, we propose a new method to estimate the diffusion function in the jump-diffusion model. First, a threshold reweighted Nadaraya–Watson-type estimator is introduced. Then, we establish asymptotic normality for the estimator and conduct Monte Carlo simulations through two examples to verify the better finite-sampling properties. Finally, our estimator is demonstrated through the actual
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Lower and upper pricing of financial assets Probab. Uncertain. Quant. Risk Pub Date : 2022-01-01 Robert Elliott,Dilip B. Madan,Tak Kuen Siu
Modeling of uncertainty by probability errs by ignoring the uncertainty in probability. When financial valuation recognizes the uncertainty of probability, the best the market may offer is a two price framework of a lower and upper valuation. The martingale theory of asset prices is then replaced by the theory of nonlinear martingales. When dealing with pure jump compensators describing probability
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Quantitative stability and numerical analysis of Markovian quadratic BSDEs with reflection Probab. Uncertain. Quant. Risk Pub Date : 2022-01-01 Dingqian Sun,Gechun Liang,Shanjian Tang
We study the quantitative stability of solutions to Markovian quadratic reflected backward stochastic differential equations (BSDEs) with bounded terminal data. By virtue of bounded mean oscillation martingale and change of measure techniques, we obtain stability estimates for the variation of the solutions with different underlying forward processes. In addition, we propose a truncated discrete-time
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On the laws of the iterated logarithm with mean-uncertainty under sublinear expectations Probab. Uncertain. Quant. Risk Pub Date : 2022-01-01 Xiaofan Guo,Shan Li,Xinpeng Li
A new Hartman–Wintner-type law of the iterated logarithm for independent random variables with mean-uncertainty under sublinear expectations is established by the martingale analogue of the Kolmogorov law of the iterated logarithm in classical probability theory.
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Extended conditional G-expectations and related stopping times Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Mingshang Hu,Shige Peng
In this paper, we extend the definition of conditional \begin{document}$ G{\text{-}}{\rm{expectation}} $\end{document} to a larger space on which the dynamical consistency still holds. We can consistently define, by taking the limit, the conditional \begin{document}$ G{\text{-}}{\rm{expectation}} $\end{document} for each random variable \begin{document}$ X $\end{document}, which is the downward limit
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Convergence of the Deep BSDE method for FBSDEs with non-Lipschitz coefficients Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Yifan Jiang,Jinfeng Li
This paper is dedicated to solving high-dimensional coupled FBSDEs with non-Lipschitz diffusion coefficients numerically. Under mild conditions, we provided a posterior estimate of the numerical solution that holds for any time duration. This posterior estimate validates the convergence of the recently proposed Deep BSDE method. In addition, we developed a numerical scheme based on the Deep BSDE method
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An FBSDE approach to market impact games with stochastic parameters Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Samuel Drapeau,Peng Luo,Alexander Schied,Dewen Xiong
In this study, we have analyzed a market impact game between n risk-averse agents who compete for liquidity in a market impact model with a permanent price impact and additional slippage. Most market parameters, including volatility and drift, are allowed to vary stochastically. Our first main result characterizes the Nash equilibrium in terms of a fully coupled system of forward-backward stochastic
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Stochastic maximum principle for systems driven by local martingales with spatial parameters Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Jian Song,Meng Wang
We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter. Assuming the convexity of the control domain, we obtain the stochastic maximum principle as the necessary condition for an optimal control, and we also prove its sufficiency under proper conditions. The stochastic linear quadratic
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Reduced-form setting under model uncertainty with non-linear affine intensities Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Francesca Biagini,Katharina Oberpriller
In this paper we extend the reduced-form setting under model uncertainty introduced in [5] to include intensities following an affine process under parameter uncertainty, as defined in [15]. This framework allows us to introduce a longevity bond under model uncertainty in a way consistent with the classical case under one prior and to compute its valuation numerically. Moreover, we price a contingent
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An infinite-dimensional model of liquidity in financial markets Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Sergey V Lototsky,Henry Schellhorn,Ran Zhao
We consider a dynamic market model of liquidity where unmatched buy and sell limit orders are stored in order books. The resulting net demand surface constitutes the sole input to the model. We model demand using a two-parameter Brownian motion because (i) different points on the demand curve correspond to orders motivated by different information, and (ii) in general, the market price of risk equation
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G-Lévy processes under sublinear expectations Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Mingshang Hu,Shige Peng
We introduce G-Levy processes which develop the theory of processes with independent and stationary increments under the framework of sublinear expectations. We then obtain the Levy-Khintchine formula and the existence for G-Levy processes. We also introduce G-Poisson processes.
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The term structure of sharpe ratios and arbitrage-free asset pricing in continuous time Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Patrick Beißner,Emanuela Rosazza Gianin
Motivated by financial and empirical arguments and in order to introduce a more flexible methodology of pricing, we provide a new approach to asset pricing based on Backward Volterra equations. The approach relies on an arbitrage-free and incomplete market setting in continuous time by choosing non-unique pricing measures depending either on the time of evaluation or on the maturity of payoffs. We
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Conditional coherent risk measures and regime-switching conic pricing Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Engel John C Dela Vega,Robert J Elliott
This paper introduces and represents conditional coherent risk measures as essential suprema of conditional expectations over a convex set of probability measures and as distorted expectations given a concave distortion function. A model is then developed for the bid and ask prices of a European-type asset by a conic formulation. The price process is governed by a modified geometric Brownian motion
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On the laws of the iterated logarithm under sub-linear expectations Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Li-Xin Zhang
In this paper, we establish some general forms of the law of the iterated logarithm for independent random variables in a sub-linear expectation space, where the random variables are not necessarily identically distributed. Exponential inequalities for the maximum sum of independent random variables and Kolmogorov’s converse exponential inequalities are established as tools for showing the law of the
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Optimal unbiased estimation for maximal distribution Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Hanqing Jin,Shige Peng
Unbiased estimation for parameters of maximal distribution is a fundamental problem in the statistical theory of sublinear expectations. In this paper, we proved that the maximum estimator is the largest unbiased estimator for the upper mean and the minimum estimator is the smallest unbiased estimator for the lower mean.
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Convergence rate of Peng’s law of large numbers under sublinear expectations Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Mingshang Hu,Xiaojuan Li,Xinpeng Li
This short note provides a new and simple proof of the convergence rate for the Peng’s law of large numbers under sublinear expectations, which improves the results presented by Song [15] and Fang et al. [3].
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Stein’s method for the law of large numbers under sublinear expectations Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Yongsheng Song
Peng, S. [6] proved the law of large numbers under a sublinear expectation. In this paper, we give its error estimates by Stein’s method.
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Existence, uniqueness and strict comparison theorems for BSDEs driven by RCLL martingales Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Tianyang Nie,Marek Rutkowski
The existence, uniqueness, and strict comparison for solutions to a BSDE driven by a multi-dimensional RCLL martingale are developed. The goal is to develop a general multi-asset framework encompassing a wide spectrum of non-linear financial models with jumps, including as particular cases, the setups studied by Peng and Xu [27, 28] and Dumitrescu et al. [7] who dealt with BSDEs driven by a one-dimensional
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General time interval multidimensional BSDEs with generators satisfying a weak stochastic-monotonicity condition Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Tingting Li,Ziheng Xu,Shengjun Fan
This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where the generator \begin{document}$ g $\end{document} satisfies a weak stochastic-monotonicity condition and a general growth condition in the state variable \begin{document}$ y $\end{document}, and a stochastic-Lipschitz
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CVaR-hedging and its applications to equity-linked life insurance contracts with transaction costs Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Alexander Melnikov,Hongxi Wan
This paper analyzes Conditional Value-at-Risk (CVaR) based partial hedging and its applications on equity-linked life insurance contracts in a Jump-Diffusion market model with transaction costs. A nonlinear partial differential equation (PDE) that an option value process inclusive of transaction costs should satisfy is provided. In particular, the closed-form expression of a European call option price
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Dual representation of expectile-based expected shortfall and its properties Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Mekonnen Tadese,Samuel Drapeau
An expectile can be considered a generalization of a quantile. While expected shortfall is a quantile-based risk measure, we study its counterpart—the expectile-based expected shortfall—where expectile takes the place of a quantile. We provide its dual representation in terms of a Bochner integral. Among other properties, we show that it is bounded from below in terms of the convex combination of expected
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Improved Hoeffding inequality for dependent bounded or sub-Gaussian random variables Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Yuta Tanoue
When addressing various financial problems, such as estimating stock portfolio risk, it is necessary to derive the distribution of the sum of the dependent random variables. Although deriving this distribution requires identifying the joint distribution of these random variables, exact estimation of the joint distribution of dependent random variables is difficult. Therefore, in recent years, studies
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Stochastic ordering by g-expectations Probab. Uncertain. Quant. Risk Pub Date : 2021-01-01 Sel Ly,Nicolas Privault
We derive sufficient conditions for the convex and monotonic g-stochastic ordering of diffusion processes under nonlinear g-expectations and g-evaluations. Our approach relies on comparison results for forward-backward stochastic differential equations and on several extensions of convexity, monotonicity and continuous dependence properties for the solutions of associated semilinear parabolic partial
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Fully nonlinear stochastic and rough PDEs: Classical and viscosity solutions Probab. Uncertain. Quant. Risk Pub Date : 2020-11-03 Rainer Buckdahn, Christian Keller, Jin Ma, Jianfeng Zhang
We study fully nonlinear second-order (forward) stochastic PDEs. They can also be viewed as forward path-dependent PDEs and will be treated as rough PDEs under a unified framework. For the most general fully nonlinear case, we develop a local theory of classical solutions and then define viscosity solutions through smooth test functions. Our notion of viscosity solutions is equivalent to the alternative
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Efficient hedging under ambiguity in continuous time Probab. Uncertain. Quant. Risk Pub Date : 2020-08-28 Ludovic Tangpi
It is well known that the minimal superhedging price of a contingent claim is too high for practical use. In a continuous-time model uncertainty framework, we consider a relaxed hedging criterion based on acceptable shortfall risks. Combining existing aggregation and convex dual representation theorems, we derive duality results for the minimal price on the set of upper semicontinuous discounted claims
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Convergence of the deep BSDE method for coupled FBSDEs Probab. Uncertain. Quant. Risk Pub Date : 2020-07-03 Jiequn Han, Jihao Long
The recently proposed numerical algorithm, deep BSDE method, has shown remarkable performance in solving high-dimensional forward-backward stochastic differential equations (FBSDEs) and parabolic partial differential equations (PDEs). This article lays a theoretical foundation for the deep BSDE method in the general case of coupled FBSDEs. In particular, a posteriori error estimation of the solution
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Uncertainty and filtering of hidden Markov models in discrete time Probab. Uncertain. Quant. Risk Pub Date : 2020-06-03 Samuel N. Cohen
We consider the problem of filtering an unseen Markov chain from noisy observations, in the presence of uncertainty regarding the parameters of the processes involved. Using the theory of nonlinear expectations, we describe the uncertainty in terms of a penalty function, which can be propagated forward in time in the place of the filter. We also investigate a simple control problem in this context
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Upper risk bounds in internal factor models with constrained specification sets Probab. Uncertain. Quant. Risk Pub Date : 2020-05-19 Jonathan Ansari, Ludger Rüschendorf
For the class of (partially specified) internal risk factor models we establish strongly simplified supermodular ordering results in comparison to the case of general risk factor models. This allows us to derive meaningful and improved risk bounds for the joint portfolio in risk factor models with dependence information given by constrained specification sets for the copulas of the risk components
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Moderate deviation for maximum likelihood estimators from single server queues Probab. Uncertain. Quant. Risk Pub Date : 2020-03-24 Saroja Kumar Singh
Consider a single server queueing model which is observed over a continuous time interval (0,T], where T is determined by a suitable stopping rule. Let θ be the unknown parameter for the arrival process and $\hat {\theta }_{T}$ be the maximum likelihood estimator of θ. The main goal of this paper is to obtain a moderate deviation result of the maximum likelihood estimator for the single server queueing
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Limit behaviour of the minimal solution of a BSDE with singular terminal condition in the non Markovian setting Probab. Uncertain. Quant. Risk Pub Date : 2020-02-19 Dmytro Marushkevych, Alexandre Popier
We use the functional Itô calculus to prove that the solution of a BSDE with singular terminal condition verifies at the terminal time: $\liminf _{t\to T} Y(t) = \xi = Y(T)$. Hence, we extend known results for a non-Markovian terminal condition.
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Nonlinear regression without i.i.d. assumption Probab. Uncertain. Quant. Risk Pub Date : 2019-11-05 Qing Xu, Xiaohua (Michael) Xuan
In this paper, we consider a class of nonlinear regression problems without the assumption of being independent and identically distributed. We propose a correspondent mini-max problem for nonlinear regression and give a numerical algorithm. Such an algorithm can be applied in regression and machine learning problems, and yields better results than traditional least squares and machine learning methods
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Publisher Correction to: Probability, uncertainty and quantitative risk, volume 4 Probab. Uncertain. Quant. Risk Pub Date : 2019-08-26
An error occurred during the publication of an article in Probability, Uncertainty and Quantitative Risk. The article was published in volume 4 with a duplicate citation number.
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Correction to: “Existence, uniqueness and comparison results for BSDEs with Lévy jumps in an extended monotonic generator setting” Probab. Uncertain. Quant. Risk Pub Date : 2019-08-15 Christel Geiss, Alexander Steinicke
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Affine processes under parameter uncertainty Probab. Uncertain. Quant. Risk Pub Date : 2019-05-28 Tolulope Fadina, Ariel Neufeld, Thorsten Schmidt
We develop a one-dimensional notion of affine processes under parameter uncertainty, which we call nonlinear affine processes. This is done as follows: given a set Θ of parameters for the process, we construct a corresponding nonlinear expectation on the path space of continuous processes. By a general dynamic programming principle, we link this nonlinear expectation to a variational form of the Kolmogorov
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Law of large numbers and central limit theorem under nonlinear expectations Probab. Uncertain. Quant. Risk Pub Date : 2019-04-16 Shige Peng
The main achievement of this paper is the finding and proof of Central Limit Theorem (CLT, see Theorem 12) under the framework of sublinear expectation. Roughly speaking under some reasonable assumption, the random sequence $\{1/\sqrt {n}(X_{1}+\cdots +X_{n})\}_{i=1}^{\infty }$ converges in law to a nonlinear normal distribution, called G-normal distribution, where $\{X_{i}\}_{i=1}^{\infty }$ is an
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The Cauchy problem of Backward Stochastic Super-Parabolic Equations with Quadratic Growth Probab. Uncertain. Quant. Risk Pub Date : 2019-03-30 Renzhi Qiu, Shanjian Tang
The paper is devoted to the Cauchy problem of backward stochastic super-parabolic equations with quadratic growth. We prove two Itô formulas in the whole space. Furthermore, we prove the existence of weak solutions for the case of one-dimensional state space, and the uniqueness of weak solutions without constraint on the state space.
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Piecewise constant martingales and lazy clocks Probab. Uncertain. Quant. Risk Pub Date : 2019-02-11 Christophe Profeta, Frédéric Vrins
Conditional expectations (like, e.g., discounted prices in financial applications) are martingales under an appropriate filtration and probability measure. When the information flow arrives in a punctual way, a reasonable assumption is to suppose the latter to have piecewise constant sample paths between the random times of information updates. Providing a way to find and construct piecewise constant
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Mixed deterministic and random optimal control of linear stochastic systems with quadratic costs Probab. Uncertain. Quant. Risk Pub Date : 2019-01-04 Ying Hu, Shanjian Tang
In this paper, we consider the mixed optimal control of a linear stochastic system with a quadratic cost functional, with two controllers—one can choose only deterministic time functions, called the deterministic controller, while the other can choose adapted random processes, called the random controller. The optimal control is shown to exist under suitable assumptions. The optimal control is characterized
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Existence, uniqueness and comparison results for BSDEs with Lévy jumps in an extended monotonic generator setting. Probab. Uncertain. Quant. Risk Pub Date : 2018-12-28 Christel Geiss,Alexander Steinicke
We show that the comparison results for a backward SDE with jumps established in Royer (Stoch. Process. Appl 116: 1358–1376, 2006) and Yin and Mao (J. Math. Anal. Appl 346: 345–358, 2008) hold under more simplified conditions. Moreover, we prove existence and uniqueness allowing the coefficients in the linear growth- and monotonicity-condition for the generator to be random and time-dependent. In the
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Optimal control with delayed information flow of systems driven by G-Brownian motion Probab. Uncertain. Quant. Risk Pub Date : 2018-10-20 Francesca Biagini, Thilo Meyer-Brandis, Bernt Øksendal, Krzysztof Paczka
In this paper, we study strongly robust optimal control problems under volatility uncertainty. In the G-framework, we adapt the stochastic maximum principle to find necessary and sufficient conditions for the existence of a strongly robust optimal control.
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Zero covariation returns Probab. Uncertain. Quant. Risk Pub Date : 2018-06-05 Dilip B. Madan, Wim Schoutens
Asset returns are modeled by locally bilateral gamma processes with zero covariations. Covariances are then observed to be consequences of randomness in variations. Support vector machine regressions on prices are employed to model the implied randomness. The contributions of support vector machine regressions are evaluated using reductions in the economic cost of exposure to prediction residuals.
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Path-dependent backward stochastic Volterra integral equations with jumps, differentiability and duality principle Probab. Uncertain. Quant. Risk Pub Date : 2018-06-05 Ludger Overbeck, Jasmin A. L. Röder
We study the existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations (BSVIEs) with jumps, where path-dependence means the dependence of the free term and generator of a path of a càdlàg process. Furthermore, we prove path-differentiability of such a solution and establish the duality principle between a linear path-dependent forward stochastic Volterra
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Pricing formulae for derivatives in insurance using Malliavin calculus Probab. Uncertain. Quant. Risk Pub Date : 2018-06-05 Caroline Hillairet, Ying Jiao, Anthony Réveillac
In this paper, we provide a valuation formula for different classes of actuarial and financial contracts which depend on a general loss process by using Malliavin calculus. Similar to the celebrated Black–Scholes formula, we aim to express the expected cash flow in terms of a building block. The former is related to the loss process which is a cumulated sum indexed by a doubly stochastic Poisson process
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Risk excess measures induced by hemi-metrics Probab. Uncertain. Quant. Risk Pub Date : 2018-06-05 Olivier P. Faugeras, Ludger Rüschendorf
The main aim of this paper is to introduce the notion of risk excess measure, to analyze its properties, and to describe some basic construction methods. To compare the risk excess of one distribution Q w.r.t. a given risk distribution P, we apply the concept of hemi-metrics on the space of probability measures. This view of risk comparison has a natural basis in the extension of orderings and hemi-metrics
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Information uncertainty related to marked random times and optimal investment Probab. Uncertain. Quant. Risk Pub Date : 2018-05-10 Ying Jiao, Idris Kharroubi
We study an optimal investment problem under default risk where related information such as loss or recovery at default is considered as an exogenous random mark added at default time. Two types of agents who have different levels of information are considered. We first make precise the insider’s information flow by using the theory of enlargement of filtrations and then obtain explicit logarithmic
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Arbitrage-free pricing of derivatives in nonlinear market models Probab. Uncertain. Quant. Risk Pub Date : 2018-04-21 Tomasz R. Bielecki, Igor Cialenco, Marek Rutkowski
The objective of this paper is to provide a comprehensive study of the no-arbitrage pricing of financial derivatives in the presence of funding costs, the counterparty credit risk and market frictions affecting the trading mechanism, such as collateralization and capital requirements. To achieve our goals, we extend in several respects the nonlinear pricing approach developed in (El Karoui and Quenez
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Continuous tenor extension of affine LIBOR models with multiple curves and applications to XVA Probab. Uncertain. Quant. Risk Pub Date : 2018-01-10 Antonis Papapantoleon, Robert Wardenga
We consider the class of affine LIBOR models with multiple curves, which is an analytically tractable class of discrete tenor models that easily accommodates positive or negative interest rates and positive spreads. By introducing an interpolating function, we extend the affine LIBOR models to a continuous tenor and derive expressions for the instantaneous forward rate and the short rate. We show that
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Good deal hedging and valuation under combined uncertainty about drift and volatility Probab. Uncertain. Quant. Risk Pub Date : 2017-12-29 Dirk Becherer, Klebert Kentia
We study robust notions of good-deal hedging and valuation under combined uncertainty about the drifts and volatilities of asset prices. Good-deal bounds are determined by a subset of risk-neutral pricing measures such that not only opportunities for arbitrage are excluded but also deals that are too good, by restricting instantaneous Sharpe ratios. A non-dominated multiple priors approach to model
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Financial asset price bubbles under model uncertainty Probab. Uncertain. Quant. Risk Pub Date : 2017-12-22 Francesca Biagini, Jacopo Mancin
We study the concept of financial bubbles in a market model endowed with a set ${\mathcal {P}}$ of probability measures, typically mutually singular to each other. In this setting, we investigate a dynamic version of robust superreplication, which we use to introduce the notions of bubble and robust fundamental value in a way consistent with the existing literature in the classical case ${\mathcal
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Portfolio optimization of credit swap under funding costs Probab. Uncertain. Quant. Risk Pub Date : 2017-12-04 Lijun Bo
We develop a dynamic optimization framework to assess the impact of funding costs on credit swap investments. A defaultable investor can purchase CDS upfronts, borrow at a rate depending on her credit quality, and invest in the money market account. By viewing the concave drift of the wealth process as a continuous function of admissible strategies, we characterize the optimal strategy in terms of
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Characterization of optimal feedback for stochastic linear quadratic control problems Probab. Uncertain. Quant. Risk Pub Date : 2017-09-27 Qi Lü, Tianxiao Wang, Xu Zhang
One of the fundamental issues in Control Theory is to design feedback controls. It is well-known that, the purpose of introducing Riccati equations in the study of deterministic linear quadratic control problems is exactly to construct the desired feedbacks. To date, the same problem in the stochastic setting is only partially well-understood. In this paper, we establish the equivalence between the
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On the compensator of the default process in an information-based model Probab. Uncertain. Quant. Risk Pub Date : 2017-09-11 Matteo Ludovico Bedini, Rainer Buckdahn, Hans-Jürgen Engelbert
This paper provides sufficient conditions for the time of bankruptcy (of a company or a state) for being a totally inaccessible stopping time and provides the explicit computation of its compensator in a framework where the flow of market information on the default is modelled explicitly with a Brownian bridge between 0 and 0 on a random time interval.
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The joint impact of bankruptcy costs, fire sales and cross-holdings on systemic risk in financial networks Probab. Uncertain. Quant. Risk Pub Date : 2017-06-26 Stefan Weber, Kerstin Weske
The paper presents a comprehensive model of a banking system that integrates network effects, bankruptcy costs, fire sales, and cross-holdings. For the integrated financial market we prove the existence of a price-payment equilibrium and design an algorithm for the computation of the greatest and the least equilibrium. The number of defaults corresponding to the greatest price-payment equilibrium is
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Credit, funding, margin, and capital valuation adjustments for bilateral portfolios Probab. Uncertain. Quant. Risk Pub Date : 2017-06-26 Claudio Albanese, Simone Caenazzo, Stéphane Crépey
We apply to the concrete setup of a bank engaged into bilateral trade portfolios the XVA theoretical framework of (Albanese and Crépey2017), whereby so-called contra-liabilities and cost of capital are charged by the bank to its clients, on top of the fair valuation of counterparty risk, in order to account for the incompleteness of this risk. The transfer of the residual reserve credit capital from
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Measure distorted arrival rate risks and their rewards Probab. Uncertain. Quant. Risk Pub Date : 2017-06-26 Dilip B. Madan
Risks embedded in asset price dynamics are taken to be accumulations of surprise jumps. A Markov pure jump model is formulated on making variance gamma parameters deterministic functions of the price level. Estimation is done by matrix exponentiation of the transition rate matrix for a continuous time finite state Markov chain approximation. The motion is decomposed into a space dependent drift and
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A brief history of quantitative finance Probab. Uncertain. Quant. Risk Pub Date : 2017-06-05 Mauro Cesa
In this introductory paper to the issue, I will travel through the history of how quantitative finance has developed and reached its current status, what problems it is called to address, and how they differ from those of the pre-crisis world.
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Backward stochastic differential equations with Young drift Probab. Uncertain. Quant. Risk Pub Date : 2017-06-05 Joscha Diehl, Jianfeng Zhang
We show the well-posedness of backward stochastic differential equations containing an additional drift driven by a path of finite q-variation with q∈[1,2). In contrast to previous work, we apply a direct fixpoint argument and do not rely on any type of flow decomposition. The resulting object is an effective tool to study semilinear rough partial differential equations via a Feynman–Kac type representation
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Stochastic global maximum principle for optimization with recursive utilities Probab. Uncertain. Quant. Risk Pub Date : 2017-03-01 Mingshang Hu
In this paper, we study the recursive stochastic optimal control problems. The control domain does not need to be convex, and the generator of the backward stochastic differential equation can contain z. We obtain the variational equations for backward stochastic differential equations, and then obtain the maximum principle which solves completely Peng’s open problem.
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Convergence to a self-normalized G-Brownian motion Probab. Uncertain. Quant. Risk Pub Date : 2017-03-01 Zhengyan Lin, Li-Xin Zhang
G-Brownian motion has a very rich and interesting new structure that nontrivially generalizes the classical Brownian motion. Its quadratic variation process is also a continuous process with independent and stationary increments. We prove a self-normalized functional central limit theorem for independent and identically distributed random variables under the sub-linear expectation with the limit process
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Implied fractional hazard rates and default risk distributions Probab. Uncertain. Quant. Risk Pub Date : 2017-03-01 Charles S. Tapiero, Pierre Vallois
Default probability distributions are often defined in terms of their conditional default probability distribution, or their hazard rate. By their definition, they imply a unique probability density function. The applications of default probability distributions are varied, including the risk premium model used to price default bonds, reliability measurement models, insurance, etc. Fractional probability