An Optimal Stopping Problem for Jump Diffusion Logistic Population Model

Discounted optimal stopping for maxima of some jump-diffusion processes∗

We present closed form solutions to some discounted optimal stopping problems for the maximum process in a model driven by a Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial problems to integro-differential freeboundary problems where the normal reflection and smooth fit may break down and the latter then be replaced by ...

An Efficient Bayesian Optimal Design for Logistic Model

Consider a Bayesian optimal design with many support points which poses the problem of collecting data with a few number of observations at each design point. Under such a scenario the asymptotic property of using Fisher information matrix for approximating the covariance matrix of posterior ML estimators might be doubtful. We suggest to use Bhattcharyya matrix in deriving the information matri...

On an Optimal Stopping Problem of Time Inhomogeneous Diffusion Processes

For given quasi-continuous functions g, h with g ≤ h and diffusion process M determined by stochastic differential equations or symmetric Dirichlet forms, characterizations of the value functions eg(s, x) = sup σ J (s,x) (σ) and ¯ w(s, x) = infτ sup σ J (s,x) (σ, τ) are well studied so far. In this paper, by using the time dependent Dirichlet forms, we generalize these results to time inhomogen...

An Optimal Stopping Problem in a Diffusion- Type Model with Delay

Optimal Stopping, Free Boundary, and American Option in a Jump-Diffusion Model

This paper considers the American put option valuation in a jumpdiffusion model and relates this optimal-stopping problem to a parabolic integrodifferential free-boundary problem, with special attention to the behavior of the optimal-stopping boundary. We study the regularity of the American option value and obtain in particular a decomposition of the American put option price as the sum of its...