[图书][B] Backward stochastic differential equations

J Zhang, J Zhang - 2017 - Springer
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On viscosity solutions of path dependent PDEs

I Ekren, C Keller, N Touzi, J Zhang - 2014 - projecteuclid.org
In this paper we propose a notion of viscosity solutions for path dependent semi-linear
parabolic PDEs. This can also be viewed as viscosity solutions of non-Markovian backward …

Stochastic control for a class of nonlinear kernels and applications

D Possamaï, X Tan, C Zhou - The Annals of Probability, 2018 - JSTOR
We consider a stochastic control problem for a class of nonlinear kernels. More precisely,
our problem of interest consists in the optimization, over a set of possibly nondominated …

Stochastic perron's method for Hamilton--Jacobi--Bellman equations

E Bayraktar, M Sirbu - SIAM Journal on Control and Optimization, 2013 - SIAM
We show that the value function of a stochastic control problem is the unique solution of the
associated Hamilton--Jacobi--Bellman equation, completely avoiding the proof of the so …

On Gerber–Shiu functions and optimal dividend distribution for a Lévy risk process in the presence of a penalty function

F Avram, Z Palmowski, MR Pistorius - 2015 - projecteuclid.org
This paper concerns an optimal dividend distribution problem for an insurance company
whose risk process evolves as a spectrally negative Lévy process (in the absence of …

The optimal equilibrium for time-inconsistent stopping problems---the discrete-time case

YJ Huang, Z Zhou - SIAM journal on control and optimization, 2019 - SIAM
We study an infinite-horizon discrete-time optimal stopping problem under nonexponential
discounting. A new method, which we call the iterative approach, is developed to find …

Optimal equilibria for time‐inconsistent stopping problems in continuous time

YJ Huang, Z Zhou - Mathematical Finance, 2020 - Wiley Online Library
For an infinite‐horizon continuous‐time optimal stopping problem under nonexponential
discounting, we look for an optimal equilibrium, which generates larger values than any …

Zero-sum path-dependent stochastic differential games in weak formulation

D Possamaï, N Touzi, J Zhang - 2020 - projecteuclid.org
We consider zero-sum stochastic differential games with possibly path-dependent volatility
controls. Unlike the previous literature, we allow for weak solutions of the state equation so …

Optimal reinsurance under the mean–variance premium principle to minimize the probability of ruin

X Liang, Z Liang, VR Young - Insurance: Mathematics and Economics, 2020 - Elsevier
We consider the problem of minimizing the probability of ruin by purchasing reinsurance
whose premium is computed according to the mean–variance premium principle, a …

Path-dependent equations and viscosity solutions in infinite dimension

A Cosso, S Federico, F Gozzi, M Rosestolato, N Touzi - 2018 - projecteuclid.org
Path-dependent partial differential equations (PPDEs) are natural objects to study when one
deals with non-Markovian models. Recently, after the introduction of the so-called pathwise …