Optimal hedging for fund and insurance managers with partially observable investment flows

Fujii, Masaaki; Takahashi, Akihiko

doi:10.1080/14697688.2014.950320

Cited by 5 publications

(2 citation statements)

References 25 publications

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“…See, for example, Schroder & Skiadas (1999) [31] as an early research. Recently, this property was applied to the mean-variance (quadratic) hedging problem by , 2014 [19,20], making use of the beautiful BSDE expression derived by Mania & Tevzadze (2003) [27]. Notice that the Riccati equation may possibly diverge in a finite time-interval in a general setup.…”

Section: Introductionmentioning

confidence: 99%

A polynomial scheme of asymptotic expansion for backward SDEs and option pricing

Fujii

2015

Quantitative Finance

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A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed. The perturbation parameter "ǫ" is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard small-diffusion asymptotic expansion method, the dynamics of variables given by the forward SDEs is treated exactly. Although it requires a special form of the quadratic covariation terms of the continuous part, it allows rather generic drift as well as jump components to exist. The resultant approximation is given by a polynomial function in terms of the unperturbed forward variables whose coefficients are uniquely specified by the solution of the recursive system of linear ODEs. Applications to a jump-extended Heston and λ-SABR models for European contingent claims, as well as the utility-optimization problem in the presence of a terminal liability are discussed.

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Section: Introductionmentioning

confidence: 99%

A polynomial scheme of asymptotic expansion for backward SDEs and option pricing

Fujii

2015

Quantitative Finance

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“…Introducing a hidden Markov process, for example, is likely to help to model possible herding behavior among the customer orders. See a related work Fujii & Takahashi (2015) [25] on the mean-variance hedging problem for fund and insurance managers.…”

Section: Discussionmentioning

confidence: 99%

Optimal Position Management for a Market Maker with Stochastic Price Impacts

Fujii

2015

SSRN Journal

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This paper deals with an optimal position management problem for a market maker who has to face uncertain customer order flows in an illiquid market, where the market maker's continuous trading incurs a stochastic linear price impact. Although the execution timing is uncertain, the market maker can also ask its OTC counterparties to transact a block trade without causing a direct price impact. We adopt quite generic stochastic processes of the securities, order flows, price impacts, quadratic penalties as well as security borrowing/lending rates. The solution of the market maker's optimal position-management strategy is represented by a stochastic Hamilton-Jacobi-Bellman equation, which can be decomposed into three (one non-linear and two linear) backward stochastic differential equations (BSDEs). We provide the verification using the standard BSDE techniques for a single security case. For a multiple-security case, we make use of the connection of the non-linear BSDE to a special type of backward stochastic Riccati differential equation (BSRDE) whose properties were studied by Bismut (1976). We also propose a perturbative approximation scheme for the resultant BSRDE, which only requires a system of linear ODEs to be solved at each expansion order. Its justification and the convergence rate are also given.

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