# American Institute of Mathematical Sciences

## A class of stochastic Fredholm-algebraic equations and applications in finance

 1 School of Economics, Sichuan University, Chengdu 610065, China 2 School of Mathematics, Sichuan University, Chengdu 610065, China

*Corresponding author: The research was supported by the NSF of China under grant 11971332 and 11931011

Received  October 2019 Revised  July 2020 Published  September 2020

A class of stochastic Fredholm-algebraic equations (SFAEs) is introduced and investigated. Like backward stochastic differential equations (BSDEs), its solution includes two parts. The interesting thing is that the first part is deterministic and constrained, even though the whole system is stochastic. Our study is mainly motivated by risk indifference pricing problem. Actually, the existing risk indifference price always keeps unchangeable with respect to initial wealth, which is economically unsatisfying. Nevertheless, here a new wealth dependent risk indifference price is proposed by particular SFAEs.

Citation: Zheng Liu, Tianxiao Wang. A class of stochastic Fredholm-algebraic equations and applications in finance. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2020267
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