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  • High-frequency trading with fractional Brownian motion
    Finance Stoch. (IF 2.048) Pub Date : 2020-10-08
    Paolo Guasoni, Yuliya Mishura, Miklós Rásonyi

    In the high-frequency limit, conditionally expected increments of fractional Brownian motion converge to a white noise, shedding their dependence on the path history and the forecasting horizon and making dynamic optimisation problems tractable. We find an explicit formula for locally mean–variance optimal strategies and their performance for an asset price that follows fractional Brownian motion.

  • Optimal reduction of public debt under partial observation of the economic growth
    Finance Stoch. (IF 2.048) Pub Date : 2020-09-15
    Giorgia Callegaro, Claudia Ceci, Giorgio Ferrari

    We consider a government that aims at reducing the debt-to-(gross domestic product) (GDP) ratio of a country. The government observes the level of the debt-to-GDP ratio and an indicator of the state of the economy, but does not directly observe the development of the underlying macroeconomic conditions. The government’s criterion is to minimise the sum of the total expected costs of holding debt and

  • Construction of a class of forward performance processes in stochastic factor models, and an extension of Widder’s theorem
    Finance Stoch. (IF 2.048) Pub Date : 2020-09-10
    Levon Avanesyan, Mykhaylo Shkolnikov, Ronnie Sircar

    We consider the problem of optimal portfolio selection under forward investment performance criteria in an incomplete market. Given multiple traded assets, the prices of which depend on multiple observable stochastic factors, we construct a large class of forward performance processes, as well as the corresponding optimal portfolios, with power-utility initial data and for stock–factor correlation

  • Extended weak convergence and utility maximisation with proportional transaction costs
    Finance Stoch. (IF 2.048) Pub Date : 2020-09-08
    Erhan Bayraktar, Leonid Dolinskyi, Yan Dolinsky

    In this paper, we study utility maximisation with proportional transaction costs. Assuming extended weak convergence of the underlying processes, we prove the convergence of the time-0 values of the corresponding utility maximisation problems. Moreover, we establish a limit theorem for the optimal trading strategies. The proofs are based on the extended weak convergence theory developed in Aldous (Weak

  • Filtration shrinkage, the structure of deflators, and failure of market completeness
    Finance Stoch. (IF 2.048) Pub Date : 2020-09-02
    Constantinos Kardaras, Johannes Ruf

    We analyse the structure of local martingale deflators projected on smaller filtrations. In a general continuous-path setting, we show that the local martingale parts in the multiplicative Doob–Meyer decomposition of projected local martingale deflators are themselves local martingale deflators in the smaller information market. Via use of a Bayesian filtering approach, we demonstrate the exact mechanism

  • Asset prices in segmented and integrated markets
    Finance Stoch. (IF 2.048) Pub Date : 2020-07-28
    Paolo Guasoni, Kwok Chuen Wong

    This paper evaluates the effect of market integration on prices and welfare, in a model where two Lucas trees grow in separate regions with similar investors. We find equilibrium asset price dynamics and welfare both in segmentation, when each region holds its own asset and consumes its dividend, and in integration, when both regions trade both assets and consume both dividends. Integration always

  • The Riesz representation theorem and weak ∗ compactness of semimartingales
    Finance Stoch. (IF 2.048) Pub Date : 2020-07-22
    Matti Kiiski

    We show that the sequential closure of a family of probability measures on the canonical space of càdlàg paths satisfying Stricker’s uniform tightness condition is a weak∗ compact set of semimartingale measures in the dual pairing of bounded continuous functions and Radon measures, that is, the dual pairing from the Riesz representation theorem under topological assumptions on the path space. Similar

  • The Leland–Toft optimal capital structure model under Poisson observations
    Finance Stoch. (IF 2.048) Pub Date : 2020-07-17
    Zbigniew Palmowski, José Luis Pérez, Budhi Arta Surya, Kazutoshi Yamazaki

    This paper revisits the optimal capital structure model with endogenous bankruptcy, first studied by Leland (J. Finance 49:1213–1252, 1994) and Leland and Toft (J. Finance 51:987–1019, 1996). Unlike in the standard case where shareholders continuously observe the asset value and bankruptcy is executed instantaneously without delay, the information of the asset value is assumed to be updated periodically

  • Optimal insurance with background risk: An analysis of general dependence structures
    Finance Stoch. (IF 2.048) Pub Date : 2020-07-14
    Yichun Chi, Wei Wei

    In this paper, we consider an optimal insurance problem from the perspective of a risk-averse individual who faces an insurable risk as well as some background risk and wants to maximise the expected utility of his/her final wealth. To reduce ex post moral hazard, we follow Huberman et al. (Bell J. Econ. 14:415–426 1983) to assume that alternative insurance contracts satisfy the principle of indemnity

  • Option valuation and hedging using an asymmetric risk function: asymptotic optimality through fully nonlinear partial differential equations
    Finance Stoch. (IF 2.048) Pub Date : 2020-06-12
    Emmanuel Gobet; Isaque Pimentel; Xavier Warin

    Discrete-time hedging produces a residual P&L, namely the tracking error. The major problem is to get valuation/hedging policies minimising this error. We evaluate the risk between trading dates through a function penalising profits and losses asymmetrically. After deriving the asymptotics from a discrete-time risk measurement for a large number of trading dates, we derive the optimal strategies minimising

  • Realised volatility and parametric estimation of Heston SDEs
    Finance Stoch. (IF 2.048) Pub Date : 2020-06-05
    Robert Azencott; Peng Ren; Ilya Timofeyev

    We present a detailed analysis of observable moment-based parameter estimators for the Heston SDEs jointly driving the rate of returns \((R_{t})\) and the squared volatilities \((V_{t})\). Since volatilities are not directly observable, our parameter estimators are constructed from empirical moments of realised volatilities \((Y_{t})\), which are of course observable. Realised volatilities are computed

  • A splitting strategy for the calibration of jump-diffusion models
    Finance Stoch. (IF 2.048) Pub Date : 2020-06-04
    Vinicius V. L. Albani; Jorge P. Zubelli

    We present a detailed analysis and implementation of a splitting strategy to identify simultaneously the local volatility surface and the jump-size distribution from quoted European prices. The underlying model consists of a jump-diffusion driven asset with time- and price-dependent volatility. Our approach uses a forward Dupire-type partial integro-differential equation for the option prices to produce

  • Adapted Wasserstein distances and stability in mathematical finance
    Finance Stoch. (IF 2.048) Pub Date : 2020-06-04
    Julio Backhoff-Veraguas; Daniel Bartl; Mathias Beiglböck; Manu Eder

    Assume that an agent models a financial asset through a measure ℚ with the goal to price/hedge some derivative or optimise some expected utility. Even if the model ℚ is chosen in the most skilful and sophisticated way, the agent is left with the possibility that ℚ does not provide an exact description of reality. This leads us to the following question: will the hedge still be somewhat meaningful for

  • Conditional Davis pricing
    Finance Stoch. (IF 2.048) Pub Date : 2020-05-18
    Kasper Larsen; Halil Mete Soner; Gordan Žitković

    We study the set of Davis (marginal utility-based) prices of a financial derivative in the case where the investor has a non-replicable random endowment. We give a new characterisation of the set of all such prices, and provide an example showing that even in the simplest of settings – such as Samuelson’s geometric Brownian motion model –, the interval of Davis prices is often a non-degenerate subinterval

  • Time reversal and last passage time of diffusions with applications to credit risk management
    Finance Stoch. (IF 2.048) Pub Date : 2020-05-18
    Masahiko Egami; Rusudan Kevkhishvili

    We study time reversal, last passage time and \(h\)-transform of linear diffusions. For general diffusions with killing, we obtain the probability density of the last passage time to an arbitrary level and analyse the distribution of the time left until killing after the last passage time. With these tools, we develop a new risk management framework for companies based on the leverage process (the

  • Fast mean-reversion asymptotics for large portfolios of stochastic volatility models
    Finance Stoch. (IF 2.048) Pub Date : 2020-05-08
    Ben Hambly; Nikolaos Kolliopoulos

    We consider an asymptotic SPDE description of a large portfolio model where the underlying asset prices evolve according to certain stochastic volatility models with default upon hitting a lower barrier. The asset prices and their volatilities are correlated through systemic Brownian motions, and the SPDE is obtained on the positive half-space along with a Dirichlet boundary condition. We study the

  • Partial liquidation under reference-dependent preferences
    Finance Stoch. (IF 2.048) Pub Date : 2020-03-16
    Vicky Henderson; Jonathan Muscat

    We propose a multiple optimal stopping model where an investor can sell a divisible asset position at times of her choosing. Investors have \(S\)-shaped reference-dependent preferences, whereby utility is defined over gains and losses relative to a reference level and is concave over gains and convex over losses. For a price process following a time-homogeneous diffusion, we employ the constructive

  • Consumption in incomplete markets
    Finance Stoch. (IF 2.048) Pub Date : 2020-03-10
    Paolo Guasoni; Gu Wang

    We develop a method to find approximate solutions, and their accuracy, to consumption–investment problems with isoelastic preferences and infinite horizon, in incomplete markets where state variables follow a multivariate diffusion. We construct upper and lower contractions; these are fictitious complete markets in which state variables are fully hedgeable, but their dynamics is distorted. Such contractions

  • Regime switching affine processes with applications to finance
    Finance Stoch. (IF 2.048) Pub Date : 2020-02-21
    Misha van Beek; Michel Mandjes; Peter Spreij; Erik Winands

    We introduce the notion of a regime switching affine process. Informally this is a Markov process that behaves conditionally on each regime as an affine process with specific parameters. To facilitate our analysis, specific restrictions are imposed on these parameters. The regime switches are driven by a Markov chain. We prove that the joint process of the Markov chain and the conditionally affine

  • Term structure modelling for multiple curves with stochastic discontinuities
    Finance Stoch. (IF 2.048) Pub Date : 2020-02-14
    Claudio Fontana; Zorana Grbac; Sandrine Gümbel; Thorsten Schmidt

    We develop a general term structure framework taking stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the jumps of the term structures in correspondence to monetary policy meetings of the ECB show. We provide a general analysis of multiple curve markets under minimal assumptions in an extended HJM framework and

  • The value of informational arbitrage
    Finance Stoch. (IF 2.048) Pub Date : 2020-02-11
    Huy N. Chau; Andrea Cosso; Claudio Fontana

    In the context of a general semimartingale model, we aim at determining how much an investor is willing to pay to learn additional information that allows achieving arbitrage. If such a value exists, we call it the value of informational arbitrage. We are interested in the case where the information yields arbitrage opportunities but not unbounded profits with bounded risk. As in Amendinger et al.

  • On fairness of systemic risk measures
    Finance Stoch. (IF 2.048) Pub Date : 2020-02-04
    Francesca Biagini; Jean-Pierre Fouque; Marco Frittelli; Thilo Meyer-Brandis

    In our previous paper “A unified approach to systemic risk measures via acceptance sets” (Mathematical Finance, 2018), we have introduced a general class of systemic risk measures that allow random allocations to individual banks before aggregation of their risks. In the present paper, we prove a dual representation of a particular subclass of such systemic risk measures and the existence and uniqueness

  • An incomplete equilibrium with a stochastic annuity
    Finance Stoch. (IF 2.048) Pub Date : 2020-01-29
    Kim Weston; Gordan Žitković

    We prove the global existence of an incomplete, continuous-time finite-agent Radner equilibrium in which exponential agents optimise their expected utility over both running consumption and terminal wealth. The market consists of a traded annuity, and along with unspanned income, the market is incomplete. Set in a Brownian framework, the income is driven by a multidimensional diffusion and in particular

  • Trading strategies generated pathwise by functions of market weights
    Finance Stoch. (IF 2.048) Pub Date : 2019-12-17
    Ioannis Karatzas; Donghan Kim

    Twenty years ago, E.R. Fernholz introduced the notion of “functional generation” to construct a variety of portfolios solely in terms of the individual companies’ market weights. I. Karatzas and J. Ruf recently developed another approach to the functional construction of portfolios which leads to very simple conditions for strong relative arbitrage with respect to the market. Here, both of these notions

  • Ruin probabilities for a Lévy-driven generalised Ornstein–Uhlenbeck process
    Finance Stoch. (IF 2.048) Pub Date : 2019-12-04
    Yuri Kabanov; Serguei Pergamenshchikov

    We study the asymptotics of the ruin probability for a process which is the solution of a linear SDE defined by a pair of independent Lévy processes. Our main interest is a model describing the evolution of the capital reserve of an insurance company selling annuities and investing in a risky asset. Let \(\beta >0\) be the root of the cumulant-generating function \(H\) of the increment \(V_{1}\) of

  • Pathwise superhedging on prediction sets
    Finance Stoch. (IF 2.048) Pub Date : 2019-11-22
    Daniel Bartl; Michael Kupper; Ariel Neufeld

    In this paper, we provide a pricing–hedging duality for the model-independent superhedging price with respect to a prediction set \(\Xi \subseteq C[0,T]\), where the superhedging property needs to hold pathwise, but only for paths lying in \(\Xi \). For any Borel-measurable claim \(\xi \) bounded from below, the superhedging price coincides with the supremum over all pricing functionals \(\mathbb{E}_{\mathbb{Q}}[

  • On the quasi-sure superhedging duality with frictions
    Finance Stoch. (IF 2.048) Pub Date : 2019-11-21
    Erhan Bayraktar; Matteo Burzoni

    We prove the superhedging duality for a discrete-time financial market with proportional transaction costs under model uncertainty. Frictions are modelled through solvency cones as in the original model of Kabanov (Finance Stoch. 3:237–248, 1999) adapted to the quasi-sure setup of Bouchard and Nutz (Ann. Appl. Probab. 25:823–859, 2015). Our approach allows removing the restrictive assumption of no

  • Optimal dividends with partial information and stopping of a degenerate reflecting diffusion
    Finance Stoch. (IF 2.048) Pub Date : 2019-10-18
    Tiziano De Angelis

    We study the optimal dividend problem for a firm’s manager who has partial information on the profitability of the firm. The problem is formulated as one of singular stochastic control with partial information on the drift of the underlying process and with absorption. In the Markovian formulation, we have a two-dimensional degenerate diffusion whose first component is singularly controlled. Moreover

  • A Black–Scholes inequality: applications and generalisations
    Finance Stoch. (IF 2.048) Pub Date : 2019-10-18
    Michael R. Tehranchi

    The space of call price curves has a natural noncommutative semigroup structure with an involution. A basic example is the Black–Scholes call price surface, from which an interesting inequality for Black–Scholes implied volatility is derived. The binary operation is compatible with the convex order, and therefore a one-parameter sub-semigroup gives rise to an arbitrage-free market model. It is shown

  • Linear credit risk models
    Finance Stoch. (IF 2.048) Pub Date : 2019-10-04
    Damien Ackerer; Damir Filipović

    We introduce a novel class of credit risk models in which the drift of the survival process of a firm is a linear function of the factors. The prices of defaultable bonds and credit default swaps (CDS) are linear–rational in the factors. The price of a CDS option can be uniformly approximated by polynomials in the factors. Multi-name models can produce simultaneous defaults, generate positively as

  • The value of a liability cash flow in discrete time subject to capital requirements
    Finance Stoch. (IF 2.048) Pub Date : 2019-09-27
    Hampus Engsner; Kristoffer Lindensjö; Filip Lindskog

    The aim of this paper is to define the market-consistent multi-period value of an insurance liability cash flow in discrete time subject to repeated capital requirements, and explore its properties. In line with current regulatory frameworks, the presented approach is based on a hypothetical transfer of the original liability and a replicating portfolio to an empty corporate entity, whose owner must

  • Extreme at-the-money skew in a local volatility model
    Finance Stoch. (IF 2.048) Pub Date : 2019-09-05
    Paolo Pigato

    We consider a local volatility model, with volatility taking two possible values, depending on the value of the underlying with respect to a fixed threshold. When the threshold is taken at the money, we establish exact pricing formulas for European call options and compute short-time asymptotics of the implied volatility surface. We derive an exact formula for the at-the-money implied volatility skew

  • Finite-horizon optimal investment with transaction costs: construction of the optimal strategies
    Finance Stoch. (IF 2.048) Pub Date : 2019-09-05
    Christoph Belak; Jörn Sass

    We revisit the problem of maximising expected utility of terminal wealth in a Black–Scholes market with proportional transaction costs. While it is known that the value function of this problem is the unique viscosity solution of the HJB equation and that the HJB equation admits a classical solution on a reduced state space, it has been an open problem to verify that these two coincide. We establish

  • Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs
    Finance Stoch. (IF 2.048) Pub Date : 2019-09-05
    Christoph Kühn; Alexander Molitor

    In discrete-time markets with proportional transaction costs, Schachermayer (Math. Financ. 14:19–48, 2004) showed that robust no-arbitrage is equivalent to the existence of a strictly consistent price system. In this paper, we introduce the concept of prospective strict no-arbitrage that is a variant of the strict no-arbitrage property from Kabanov et al. (Finance Stoch. 6:371–382, 2002). The prospective

  • Risk sharing for capital requirements with multidimensional security markets
    Finance Stoch. (IF 2.048) Pub Date : 2019-08-12
    Felix-Benedikt Liebrich; Gregor Svindland

    We consider the risk sharing problem for capital requirements induced by capital adequacy tests and security markets. The agents involved in the sharing procedure may be heterogeneous in that they apply varying capital adequacy tests and have access to different security markets. We discuss conditions under which there exists a representative agent. Thereafter, we study two frameworks of capital adequacy

  • Financial risk measures for a network of individual agents holding portfolios of light-tailed objects
    Finance Stoch. (IF 2.048) Pub Date : 2019-07-26
    Claudia Klüppelberg; Miriam Isabel Seifert

    We investigate a financial network of agents holding portfolios of independent light-tailed risky objects whose losses are asymptotically exponentially distributed with distinct tail parameters. We show that the asymptotic distributions of portfolio losses belong to the class of functional exponential mixtures which we introduce in this paper. We also provide results for value-at-risk and expected

  • An application of fractional differential equations to risk theory
    Finance Stoch. (IF 2.048) Pub Date : 2019-07-12
    Corina D. Constantinescu; Jorge M. Ramirez; Wei R. Zhu

    This paper defines a new class of fractional differential operators alongside a family of random variables whose density functions solve fractional differential equations equipped with these operators. These equations can be further used to construct fractional integro-differential equations for the ruin probabilities in collective renewal risk models, with inter-arrival time distributions from the

  • Dual utilities on risk aggregation under dependence uncertainty
    Finance Stoch. (IF 2.048) Pub Date : 2019-07-05
    Ruodu Wang; Zuo Quan Xu; Xun Yu Zhou

    Finding the worst-case value of a preference over a set of plausible models is a well-established approach to address the issue of model uncertainty or ambiguity. In this paper, we study the worst-case evaluation of Yaari dual utility functionals of an aggregate risk under dependence uncertainty along with its decision-theoretic implications. To arrive at our main findings, we introduce a technical

  • The self-financing equation in limit order book markets
    Finance Stoch. (IF 2.048) Pub Date : 2019-06-12
    René Carmona; Kevin Webster

    The goal of this paper is to present a mathematical framework for trading on a limit order book, including its associated transaction costs, and to propose continuous-time equations which generalise the self-financing relationships of frictionless markets. These equations naturally differentiate between trading via limit and via market orders, as they include a price impact or adverse selection constraint

  • Forward transition rates
    Finance Stoch. (IF 2.048) Pub Date : 2019-06-11
    Kristian Buchardt; Christian Furrer; Mogens Steffensen

    The idea of forward rates stems from interest rate theory. It has natural connotations to transition rates in multi-state models. The generalisation from the forward mortality rate in a survival model to multi-state models is non-trivial and several definitions have been proposed. We establish a theoretical framework for the discussion of forward rates. Furthermore, we provide a novel definition with

  • An SPDE model for systemic risk with endogenous contagion
    Finance Stoch. (IF 2.048) Pub Date : 2019-06-10
    Ben Hambly; Andreas Søjmark

    We propose a dynamic mean-field model for ‘systemic risk’ in large financial systems, derived from a system of interacting diffusions on the positive half-line with an absorbing boundary at the origin. These diffusions represent the distances-to-default of financial institutions, and absorption at zero corresponds to default. As a way of modelling correlated exposures and herd behaviour, we consider

  • Multi-dimensional optimal trade execution under stochastic resilience
    Finance Stoch. (IF 2.048) Pub Date : 2019-05-30
    Ulrich Horst; Xiaonyu Xia

    We provide a general framework for analysing multi-dimensional portfolio liquidation problems with instantaneous and persistent price impact and stochastic resilience. We show that the value function can be described by a system of multi-dimensional backward stochastic Riccati differential equations (BSRDEs) with a singular terminal condition. We prove the existence of a solution to the BSRDE system

  • Duality for pathwise superhedging in continuous time
    Finance Stoch. (IF 2.048) Pub Date : 2019-05-29
    Daniel Bartl; Michael Kupper; David J. Prömel; Ludovic Tangpi

    We provide a model-free pricing–hedging duality in continuous time. For a frictionless market consisting of \(d\) risky assets with continuous price trajectories, we show that the purely analytic problem of finding the minimal superhedging price of a path-dependent European option has the same value as the purely probabilistic problem of finding the supremum of the expectations of the option over all

  • A multi-asset investment and consumption problem with transaction costs
    Finance Stoch. (IF 2.048) Pub Date : 2019-05-28
    David Hobson; Alex S. L. Tse; Yeqi Zhu

    In this article, we study a multi-asset version of the Merton investment and consumption problem with CRRA utility and proportional transaction costs. We specialise to a case where transaction costs are zero except for sales and purchases of a single asset which we call the illiquid asset. We show that the underlying HJB equation can be transformed into a boundary value problem for a first order differential

  • Distributional compatibility for change of measures
    Finance Stoch. (IF 2.048) Pub Date : 2019-05-28
    Jie Shen; Yi Shen; Bin Wang; Ruodu Wang

    In this paper, we characterise compatibility of distributions and probability measures on a measurable space. For a set of indices \(\mathcal{J}\), we say that the tuples of probability measures \((Q_{i})_{i\in \mathcal{J}} \) and distributions \((F_{i})_{i\in \mathcal{J}} \) are compatible if there exists a random variable having distribution \(F_{i}\) under \(Q_{i}\) for each \(i\in \mathcal{J}\)

  • Affine forward variance models
    Finance Stoch. (IF 2.048) Pub Date : 2019-05-24
    Jim Gatheral; Martin Keller-Ressel

    We introduce the class of affine forward variance (AFV) models of which both the conventional Heston model and the rough Heston model are special cases. We show that AFV models can be characterised by the affine form of their cumulant-generating function, which can be obtained as solution of a convolution Riccati equation. We further introduce the class of affine forward order flow intensity (AFI)

  • Laws of large numbers for Hayashi–Yoshida-type functionals
    Finance Stoch. (IF 2.048) Pub Date : 2019-05-10
    Ole Martin; Mathias Vetter

    The main object in the statistical analysis of high-frequency financial data are sums of functionals of increments of stochastic processes, and statistical inference is based on the asymptotic behaviour of these sums as the mesh of the observation times tends to zero. Inspired by the famous Hayashi–Yoshida estimator for the quadratic covariation based on two asynchronously observed stochastic processes

  • Robust utility maximisation in markets with transaction costs
    Finance Stoch. (IF 2.048) Pub Date : 2019-04-23
    Huy N. Chau; Miklós Rásonyi

    We consider a continuous-time market with proportional transaction costs. Under appropriate assumptions, we prove the existence of optimal strategies for investors who maximise their worst-case utility over a class of possible models. We consider utility functions defined on either the positive axis or the whole real line.

  • Sensitivity analysis of the utility maximisation problem with respect to model perturbations
    Finance Stoch. (IF 2.048) Pub Date : 2019-04-19
    Oleksii Mostovyi; Mihai Sîrbu

    We consider the expected utility maximisation problem and its response to small changes in the market price of risk in a continuous semimartingale setting. Assuming that the preferences of a rational economic agent are modelled by a general utility function, we obtain a second-order expansion of the value function, a first-order approximation of the terminal wealth, and we construct trading strategies

  • Some no-arbitrage rules under short-sales constraints, and applications to converging asset prices
    Finance Stoch. (IF 2.048) Pub Date : 2019-03-12
    Delia Coculescu; Monique Jeanblanc

    Under short-sales prohibitions, no free lunch with vanishing risk (NFLVRS) is known to be equivalent to the existence of an equivalent supermartingale measure for the price process (Pulido in Ann. Appl. Probab. 24:54–75, 2014). We give a necessary condition for the drift of a price process to satisfy NFLVRS. For two given price processes, we introduce the concept of fundamental supermartingale measure

  • Robust bounds for the American put
    Finance Stoch. (IF 2.048) Pub Date : 2019-03-05
    David Hobson; Dominykas Norgilas

    We consider the problem of finding a model-free upper bound on the price of an American put given the prices of a family of European puts on the same underlying asset. Specifically, we assume that the American put must be exercised at either \(T_{1}\) or \(T_{2}\) and that we know the prices of all vanilla European puts with these maturities. In this setting, we find a model which is consistent with

  • Estimating the Hurst parameter from short term volatility swaps: a Malliavin calculus approach
    Finance Stoch. (IF 2.048) Pub Date : 2019-03-01
    Elisa Alòs; Kenichiro Shiraya

    This paper is devoted to studying the difference between the fair strike of a volatility swap and the at-the-money implied volatility (ATMI) of a European call option. It is well known that the difference between these two quantities converges to zero as the time to maturity decreases. In this paper, we make use of a Malliavin calculus approach to derive an exact expression for this difference. This

  • Incorporating signals into optimal trading
    Finance Stoch. (IF 2.048) Pub Date : 2019-02-14
    Charles-Albert Lehalle; Eyal Neuman

    We incorporate a Markovian signal in the optimal trading framework which was initially proposed by Gatheral et al. (Math. Finance 22:445–474, 2012) and provide results on the existence and uniqueness of an optimal trading strategy. Moreover, we derive an explicit singular optimal strategy for the special case of an Ornstein–Uhlenbeck signal and an exponentially decaying transient market impact. The

  • Consumption, investment and healthcare with aging
    Finance Stoch. (IF 2.048) Pub Date : 2019-02-08
    Paolo Guasoni; Yu-Jui Huang

    This paper solves the problem of optimal dynamic investment, consumption and healthcare spending with isoelastic utility, when natural mortality grows exponentially to reflect the Gompertz law and investment opportunities are constant. Healthcare slows the natural growth of mortality, indirectly increasing utility from consumption through longer lifetimes. Optimal consumption and healthcare imply an

  • Utility maximisation in a factor model with constant and proportional transaction costs
    Finance Stoch. (IF 2.048) Pub Date : 2018-12-19
    Christoph Belak; Sören Christensen

    We study the problem of maximising expected utility of terminal wealth under constant and proportional transaction costs in a multidimensional market with prices driven by a factor process. We show that the value function is the unique viscosity solution of the associated quasi-variational inequalities and construct optimal strategies. While the value function turns out to be truly discontinuous, we

  • On the free boundary of an annuity purchase
    Finance Stoch. (IF 2.048) Pub Date : 2018-12-19
    Tiziano De Angelis; Gabriele Stabile

    It is known that the decision to purchase an annuity may be associated to an optimal stopping problem. However, little is known about optimal strategies if the mortality force is a generic function of time and the subjective life expectancy of the investor differs from the objective one adopted by insurance companies to price annuities. In this paper, we address this problem by considering an individual

  • A paradox in time-consistency in the mean–variance problem?
    Finance Stoch. (IF 2.048) Pub Date : 2018-12-19
    Alain Bensoussan; Kwok Chuen Wong; Sheung Chi Phillip Yam

    We establish new conditions under which a constrained (no short-selling) time-consistent equilibrium strategy, starting at a certain time, will beat the unconstrained counterpart, as measured by the magnitude of their corresponding equilibrium mean–variance value functions. We further show that the pure strategy of solely investing in a risk-free bond can sometimes simultaneously dominate both constrained

  • An ergodic BSDE approach to forward entropic risk measures: representation and large-maturity behavior
    Finance Stoch. (IF 2.048) Pub Date : 2018-12-12
    Wing Fung Chong; Ying Hu; Gechun Liang; Thaleia Zariphopoulou

    Using elements from the theory of ergodic backward stochastic differential equations (BSDEs), we study the behavior of forward entropic risk measures in stochastic factor models. We derive general representation results (via both BSDEs and convex duality) and examine their asymptotic behavior for risk positions of large maturities. We also compare them with their classical counterparts and provide

  • Minimax theorems for American options without time-consistency
    Finance Stoch. (IF 2.048) Pub Date : 2018-11-26
    Denis Belomestny; Tobias Hübner; Volker Krätschmer; Sascha Nolte

    In this paper, we give sufficient conditions guaranteeing the validity of the well-known minimax theorem for the lower Snell envelope. Such minimax results play an important role in the characterisation of arbitrage-free prices of American contingent claims in incomplete markets. Our conditions do not rely on the notions of stability under pasting or time-consistency and reveal some unexpected connection

  • A two-dimensional control problem arising from dynamic contracting theory
    Finance Stoch. (IF 2.048) Pub Date : 2018-11-08
    Jean-Paul Décamps; Stéphane Villeneuve

    We study a dynamic corporate finance contracting model in which the firm’s profitability fluctuates and is impacted by the unobservable managerial effort. Thereby, we introduce in an agency framework the issue of strategic liquidation. We show that the principal’s problem takes the form of a two-dimensional fully degenerate Markov control problem. We prove regularity properties of the value function

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