A Probabilistic Method for a Class of Non-Lipschitz BSDEs with Application to Fund Management

Han, Jinhui; Yam, Philip

doi:10.1137/21m140609x

Cited by 3 publications

(1 citation statement)

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“…If the filtration {H t } 0≤t≤T in Theorem 10 is not the augmentation of the natural filtration of W H (t), or the coefficients of the generator f L are not necessarily bounded, we refer to [37][38][39][40][41] for further results. In those cases, the existence and uniqueness of the solution to the BSDE (59) still hold under mild conditions when a general martingale representation property was assumed, or a transposition solution was considered, or a stochastic Lipschitzs condition was considered.…”

Section: Remarkmentioning

confidence: 99%

Malliavin Calculus and Its Application to Robust Optimal Investment for an Insider

Yu,

Cheng

2023

Mathematics

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In the theory of portfolio selection, there are few methods that effectively address the combined challenge of insider information and model uncertainty, despite numerous methods proposed for each individually. This paper studies the problem of the robust optimal investment for an insider under model uncertainty. To address this, we extend the Itô formula for forward integrals by Malliavin calculus, and use it to establish an implicit anticipating stochastic differential game model for the robust optimal investment. Since traditional stochastic control theory proves inadequate for solving anticipating control problems, we introduce a new approach. First, we employ the variational method to convert the original problem into a nonanticipative stochastic differential game problem. Then we use the stochastic maximum principle to derive the Hamiltonian system governing the robust optimal investment. In cases where the insider information filtration is of the initial enlargement type, we derive the closed-form expression for the investment by using the white noise theory when the insider is ’small’. When the insider is ’large’, we articulate a quadratic backward stochastic differential equation characterization of the investment. We present the numerical result and conduct an economic analysis of the optimal strategy across various scenarios.

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