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  • 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

    更新日期:2020-07-28
  • 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

    更新日期:2020-07-24
  • 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

    更新日期:2020-07-24
  • 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

    更新日期:2020-07-24
  • 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

    更新日期:2020-07-24
  • 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

    更新日期:2020-07-24
  • 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

    更新日期:2020-07-24
  • 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

    更新日期:2020-07-24
  • 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

    更新日期:2020-07-24
  • 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

    更新日期:2020-07-24
  • 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

    更新日期:2020-05-08
  • 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

    更新日期:2020-03-16
  • 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

    更新日期:2020-03-10
  • 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

    更新日期:2020-02-21
  • 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

    更新日期:2020-02-14
  • 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.

    更新日期:2020-02-11
  • 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

    更新日期:2020-02-04
  • 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

    更新日期:2020-01-29
  • 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

    更新日期:2019-12-17
  • 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}}[

    更新日期:2019-11-22
  • 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

    更新日期:2019-09-27
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