6 papers
Dynamic star-shaped risk measures and -expectations
Dejian Tian, Xunlian Wang
Motivated by the results of static monetary or star-shaped risk measures, the paper investigates the representation theorems in the dynamic framework. We show that dynamic monetary…
Robust optimized certainty equivalents and quantiles for loss positions with distribution uncertainty
Weiwei Li, Zixin Feng, Dejian Tian
This paper investigates the robust optimized certainty equivalents and analyzes their properties as risk measures under distribution uncertainty. Building on this, robust generaliz…
Pricing principle via Tsallis relative entropy in incomplete market
Dejian Tian
A pricing principle is introduced for non-attainable -exponential bounded contingent claims in an incomplete Brownian motion market setting. The buyer evaluates the contingent c…
Optimal consumption and portfolio selection with Epstein-Zin utility under general constraints
Zixin Feng, Dejian Tian
The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. Closed, not necessarily convex, constraints are imposed…
Stochastic differential games with state constraints and Isaacs equations with nonlinear Neumann problems
Lishun Xiao, Dejian Tian
We investigate a two-player zero-sum stochastic differential game problem with the state process being constrained in a connected bounded closed domain, and the cost functional des…
Probabilistic interpretation of HJB equations by the representation theorem for generators of BSDEs
Lishun Xiao, Shengjun Fan, Dejian Tian
The purpose of this note is to propose a new approach for the probabilistic interpretation of Hamilton-Jacobi-Bellman equations associated with stochastic recursive optimal control…