19,342 research outputs found
Mean-Variance Asset-Liability Management with State-Dependent Risk Aversion
In this paper, we consider the asset-liability management under the
mean-variance criterion. The financial market consists of a risk-free bond and
a stock whose price process is modeled by a geometric Brownian motion. The
liability of the investor is uncontrollable and is modeled by another geometric
Brownian motion. We consider a specific state-dependent risk aversion which
depends on a power function of the liability. By solving a flow of FBSDEs with
bivariate state process, we obtain the equilibrium strategy among all the
open-loop controls for this time-inconsistent control problem. It shows that
the equilibrium strategy is a feedback control of the liability.Comment: 12 figure
On the Dividend Strategies with Non-Exponential Discounting
In this paper, we study the dividend strategies for a shareholder with
non-constant discount rate in a diffusion risk model. We assume that the
dividends can only be paid at a bounded rate and restrict ourselves to the
Markov strategies. This is a time inconsistent control problem. The extended
HJB equation is given and the verification theorem is proved for a general
discount function. Considering the pseudo-exponential discount functions (Type
I and Type II), we get the equilibrium dividend strategies and the equilibrium
value functions by solving the extended HJB equations.Comment: 2 figure
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