arXiv subjects

Masahiko Egami

Publications and source records attributed to Masahiko Egami.

23 records · Page 2Linked to original sources

arXiv2007

Optimizing Venture Capital Investments in a Jump Diffusion Model

We study a practical optimization problems for venture capital investments and/or Research and Development (R&D) investments. The first problem is that, given the amount of the initial investment and the reward function at the initial public offering (IPO) market, the venture capitalist wants to maximize overall discounted cash flows after subtracting subsequent (if needed) investments. We describe this problem as a mixture of singular stochastic control and optimal stopping problems and give an explicit solution. The former corresponds to finding an optimal subsequent investment policy for the purpose that the value of the investee company stays away from zero. The latter corresponds to finding an optimal stopping rule in order to maximize the harvest of their investments. The second kind problem is concerned about optimal dividend policy. Rather than selling the holding stock, the investor may extract dividends when it is appropriate. We will find a quasi-explicit optimal solution to this problem and prove the existence and uniqueness of the solution and the optimality of the proposed strategy.

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arXiv2007

A Direct Method for Solving Optimal Switching Problems of One-Dimensional Diffusions

In this paper, we propose a direct solution method for optimal switching problems of one-dimensional diffusions. This method is free from conjectures about the form of the value function and switching strategies, or does not require the proof of optimality through quasi-variational inequalities. The direct method uses a general theory of optimal stopping problems for one-dimensional diffusions and characterizes the value function as sets of the smallest linear majorants in their respective transformed spaces.

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arXiv2007

The Effects of Implementation Delay on Decision-Making Under Uncertainty

In this paper, we accomplish two objectives: First, we provide a new mathematical characterization of the value function for impulse control problems with implementation delay and present a direct solution method that differs from its counterparts that use quasi-variational inequalities. Our method is direct, in the sense that we do not have to guess the form of the solution and we do not have to prove that the conjectured solution satisfies conditions of a verification lemma. Second, by employing this direct solution method, we solve two examples that involve decision delays: an exchange rate intervention problem and a problem of labor force optimization.

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arXiv2007

An Analysis of Monotone Follower Problems for Diffusion Processes

We consider a singular stochastic control problem, which is called the Monotone Follower Stochastic Control Problem and give sufficient conditions for the existence and uniqueness of a local-time type optimal control. To establish this result we use a methodology that has not been employed to solve singular control problems. We first confine ourselves to local time strategies. Then we apply a transformation to the total reward accrued by reflecting the diffusion at a given boundary and show that it is linear in its continuation region. Now, the problem of finding the optimal boundary becomes a non-linear optimization problem: The slope of the linear function and an obstacle function need to be simultaneously maximized. The necessary conditions of optimality come from first order derivative conditions. We show that under some weak assumptions these conditions become sufficient. We also show that the local time strategies are optimal in the class of all monotone increasing controls. As a byproduct of our analysis, we give sufficient conditions for the value function to be $\mathbf{C}^2$ on all its domain. We solve two dividend payment problems to show that our sufficient conditions are satisfied by the examples considered in the mainstream literature. We show that our assumptions are satisfied not only when capital of a company is modeled by a Brownian motion with drift but also when we change the modeling assumptions and use a square root process to model the capital.

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arXiv2007

A Direct Solution Method for Stochastic Impulse Control Problems of One-dimensional Diffusions

We consider stochastic impulse control problems where the process is driven by a general one-dimensional diffusion. We shall show a new mathematical characterization of the value function as a linear function in a certain transformed space. Our approach can relieve us from the burden of guessing and proving the optimal strategy, (2) present a simple method to find the value function and the corresponding control policies, and (3) handle systematically a broader class of reward and cost functions since the existence of the value function can be shown in much a simpler way.

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