Abstract
In this paper we consider an equity-indexed annuity (EIA) investor who wants to determine
when he should surrender the EIA in order to maximize his logarithmic utility of the wealth
at surrender time. We model the dynamics of the index using a geometric Brownian motion
with regime switching. To be more realistic, we consider a finite time horizon and assume
that the Markov chain is unobservable. This leads to the optimal stopping problem with
partial information. We give a representation of the value function and an integral equation
satisfied by the boundary. In the Bayesian case which is a special case of our model, we
obtain analytical results for the value function and the boundary
when he should surrender the EIA in order to maximize his logarithmic utility of the wealth
at surrender time. We model the dynamics of the index using a geometric Brownian motion
with regime switching. To be more realistic, we consider a finite time horizon and assume
that the Markov chain is unobservable. This leads to the optimal stopping problem with
partial information. We give a representation of the value function and an integral equation
satisfied by the boundary. In the Bayesian case which is a special case of our model, we
obtain analytical results for the value function and the boundary
| Original language | English |
|---|---|
| Pages (from-to) | 1251-1258 |
| Journal | Statistics and Probability Letters |
| Volume | 82 |
| DOIs | |
| Publication status | Published - 2012 |
| Externally published | Yes |