Optimal selling rules in a regime-switching exponential Gaussian diffusion model

This paper develops optimal selling rules in asset trading using a regime-switching exponential Gaussian diffusion model. The optimization problem is solved by a combined approach of boundary value problems and probabilistic analysis. A system of linear differential equations with variable coefficients and two-point boundary conditions, satisfied by the objective function of the problem, is derived. The existence and uniqueness of the solution are proved. A closed-form solution in terms of Weber functions is obtained for one-dimensional cases. For m-dimensional cases, a stochastic recursive algorithm for numerically searching the optimal value is developed. Numerical results are reported

Upper and lower solutions for regime-switching diffusions with applications in financial mathematics

This paper develops a method of upper and lower solutions for a general system of second-order ordinary differential equations with two-point boundary conditions. Our motivation of study stems from a class of financial mathematics problems under regime-switching diffusion models. Two examples are double barrier option valuation and optimal selling rules in asset trading. We establish the existence of a unique C2 solution of the two-point boundary value problem. We construct monotone sequences of upper and lower solutions that are shown to converge to the unique solution of the boundary value problem. This construction provides a feasible numerical method to compute approximate solutions. An important feature of the proposed numerical method is that the unique solution is bracketed by the upper and lower approximate solutions, which provide an interval estimate of the unique solution function. We apply the general results to a regime-switching mean-reverting model and improve related results already reported in the literature. For the mean-reverting model, explicit upper and lower solutions are obtained and numerical integration methods are employed. In another case (Example 3 in section 5) a different regime-switching model is considered, where the general results apply, but only the upper solution is explicitly obtained. In that example, only the sequence of upper solutions is numerically constructed using finite difference methods. Numerical results are reported

Optimal stopping problems with regime switching: a viscosity solution method

We employ the viscosity solution technique to analyze optimal stopping problems with regime switching. Specifically, we obtain the viscosity property of value functions, the uniqueness of viscosity solutions, the regularity of value functions and the form of optimal stopping intervals. Finally, we provide an application of the results.Comment: 29 pages, 1 figur

Pricing Liquidity Risk with Heterogeneous Investment Horizons

We develop an asset pricing model with stochastic transaction costs and investors with heterogeneous horizons. Depending on their horizon, investors hold different sets of assets in equilibrium. This generates segmentation and spillover effects for expected returns, where the liquidity (risk) premium of illiquid assets is determined by investor horizons and the correlation between liquid and illiquid asset returns. We estimate our model for the cross-section of U.S. stock returns and find that it generates a good fit, mainly due to a combination of a substantial expected liquidity premium and segmentation effects, while the liquidity risk premium is small

Conditional Efficacy of Sterilized Intervention

The noise-trading or coordination channel hypothesis implies that sterilized intervention in the foreign exchange market is effective if certain conditions are satisfied, but ineffective otherwise. The hypothesis is tested with a three-regime threshold model and daily data on actual intervention by US and German central banks. The main finding is that if central banks choose the optimal timing in light of the trend-chasing behaviors of noise traders, such strategic intervention is effective in moving the exchange rate in the desired direction.Central bank intervention; Threshold model; Coordination channel