## Abstract

A risk-minimizing approach to pricing contingent claims in a general non-Markovian, regime-switching, jump-diffusion model is discussed, where a convex risk measure is used to describe risk. The pricing problem is formulated as a two-person, zero-sum, stochastic differential game between the seller of a contingent claim and the market, where the latter may be interpreted as a "fictitious" player. A backward stochastic differential equation (BSDE) approach is applied to discuss the game problem. Attention is given to the entropic risk measure, which is a particular type of convex risk measures. In this situation, a pricing kernel selected by an equilibrium state of the game problem is related to the one selected by the Esscher transform, which was introduced to the option-pricing world in the seminal work by [38].

Original language | English |
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Pages (from-to) | 2595-2626 |

Number of pages | 32 |

Journal | Discrete and Continuous Dynamical Systems - Series B |

Volume | 22 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1 Sep 2017 |

## Keywords

- Backward stochastic differential equations
- Convex risk measures
- Esscher transforms
- Game theory
- Non-Markovian regime-switching jump diffusion
- Option valuation