Timing of Convertible Debt Financing and Investment

In this paper, we examine the optimal investment policy of the firm which is financed by issuing equity, straight debt and convertible debt. We extend the model in Mauer and Sarkar (2005) over financing with convertible debt. We examine two different investment policies that maximize the equity value and the firm value and show the agency cost as the difference between each policy value. Furthermore, we investigate how the issuance of convertible debt affects investment.

Piecewise linear Markov decision processes with an application to partially observable Markov models

This dissertation applies policy improvement and successive approximation or value iteration to a general class of Markov decision processes with discounted costs. In particular, a class of Markov decision processes, called piecewise-linear, is studied. Piecewise-linear processes are characterized by the property that the value function of a process observed for one period and then terminated is piecewise-linear if the terminal reward function is piecewise-linear. Partially observable Markov decision processes have this property. It is shown that there are e-optimal piecewise-linear value functions and piecewise-constant policies which are simple. Simple means that there are only finitely many pieces, each of which is defined on a convex polyhedral set. Algorithms based on policy improvement and successive approximation are developed to compute simple approximations to an optimal policy and the optimal value function.Business, Sauder School ofGraduat

Callable Russian Options and Their Optimal Boundaries

We deal with the pricing of callable Russian options. A callable Russian option is a contract in which both of the seller and the buyer have the rights to cancel and to exercise at any time, respectively. The pricing of such an option can be formulated as an optimal stopping problem between the seller and the buyer, and is analyzed as Dynkin game. We derive the value function of callable Russian options and their optimal boundaries