This paper is devoted to the study of optimization of investment, consumption and proportional reinsurance for an insurer with option type payoff at the terminal time under the criterion of exponential utility maximization. The surplus process of the insurer and the financial risky asset process...

In this paper, we study a kind of system of second order quasilinear parabolic partial differential equation combined with algebra equations. Introducing a family of coupled forward–backward stochastic differential equations, and by virtue of some delicate analysis techniques, we give a...

In this paper, we provide a new representation result for dynamic capital allocations and dynamic convex risk measures that are based on backward stochastic differential equations (BSDEs). We derive this representation from a classical differentiability result for BSDEs and the full allocation...

In a recent paper, Soner, Touzi and Zhang (2012) [19] have introduced a notion of second order backward stochastic differential equations (2BSDEs), which are naturally linked to a class of fully non-linear PDEs. They proved existence and uniqueness for a generator which is uniformly Lipschitz in...

The credit crisis and the ongoing European sovereign debt crisis have highlighted the native form of credit risk, namely the counterparty risk. The related credit valuation adjustment (CVA), debt valuation adjustment (DVA), liquidity valuation adjustment (LVA) and replacement cost (RC) issues,...

Under the most elementary conditions on stochastic differential equations and some milder conditions on backward stochastic differential equations with finite or infinite time intervals and linear-growth generators, a representation theorem of generators and a converse comparison theorem of...