Wulin Suo

Optimal production planning in a stochastic manufacturing system with long-run average cost

This paper is concerned with the optimal production planning in a dynamic stochastic manufacturing system consisting of a single machine that is failure prone and facing a constant demand. The objective is to choose the rate of production over time in order to minimize the long-run average cost of production and surplus. The analysis proceeds with a study of the corresponding problem with a discounted cost. It is shown using the vanishing discount approach that the Hamilton–Jacobi–Bellman equation for the average cost problem has a solution giving rise to the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem. Finally, the optimal control policy is specified in terms of the potential function.

Singular Optimal Stochastic Controls I: Existence

We apply the compactification method to study the control problem where the state is governed by an Ito stochastic differential equation allowing both classical and singular control. The problem is reformulated as a martingale problem on an appropriate canonical space after the relaxed form of the classical control is introduced. Under some mild continuity hypotheses on the data, it is shown by purely probabilistic arguments that an optimal control for the problem exists. The value function is shown to be Borel measurable.

Volatility surfaces: theory, rules of thumb, and empirical evidence

Implied volatilities are frequently used to quote the prices of options. The implied volatility of a European option on a particular asset as a function of strike price and time to maturity is known as the assets volatility surface. Traders monitor movements in volatility surfaces closely. In this paper we develop a no-arbitrage condition for the evolution of a volatility surface. We examine a number of rules of thumb used by traders to manage the volatility surface and test whether they are consistent with the no-arbitrage condition and with data on the trading of options on the S&P 500 taken from the over-the-counter market. Finally we estimate the factors driving the volatility surface in a way that is consistent with the no-arbitrage condition.

Singular Optimal Stochastic Controls II: Dynamic Programming

The dynamic programming principle for a multidimensional singular stochastic control problem is established in this paper. When assuming Lipschitz continuity on the data, it is shown that the value function is continuous and is the unique viscosity solution of the corresponding Hamilton--Jacobi--Bellman equation.

Optimal Production Planning in a Multi-Product StochasticManufacturing System with Long-Run Average Cost

This paper is concerned with the problem of production planning in a flexible manufacturing system consisting of a single or parallel failure-prone machines producing a number of different products. The objective is to choose the rates of production of the various products over time in order to meet their demands at the minimum long-run average cost of production and surplus. The analysis proceeds with a study of the corresponding problem with a discounted cost. It is shown using the vanishing discount approach for the average cost problem that the Hamilton-Jacobi-Bellman equation in terms of directional derivatives has a solution consisting of the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem, and in specifying an optimal control policy in terms of the potential function. The results settle a hitherto open problem as well as generalize known results.

Existence of singular optimal control laws for stochastic differential equations

This paper studies the existence of a control problem where the state is governed by a stochastic differential equation allowing both classical control and singular control. By transforming it into a new problem that involves only classical control, it is shown that there exists an optimal control where the classical control variable is in Markovian form and the increment of the singular control variable on any time interval is adapted to the state process on the same time interval.

Explaining Debt Recovery Using an Endogenous Bankruptcy Model

Drawing on a large sample of defaulted corporate debt from 1996 to 2007, we find that the debt recovery estimated using the Leland-Toft endogenous bankruptcy model has strong explanatory power on the debt recovery observed in the market. Our results hold after firm characteristics, industry distress, and macroeconomic conditions are taken into account. In addition, we find that both agency problems and heterogeneous bankruptcy costs weaken the explanatory power of the model. Our study suggests structural models that incorporate the role of managers in endogenously determining the bankruptcy boundary provide statistical power in explaining cross-sectional variation of corporate debt recovery.

Minimum average-cost production plan in a multi-product stochastic manufacturing system

This paper is concerned with the problem of production planning in a flexible manufacturing system consisting of a single or parallel failure-prone machines producing a number of different products. The objective is to choose the rates of production of the various products over time in order to meet their demands at the minimum long-run average cost of production and surplus. It is shown using the vanishing discount approach for the average cost problem that the Hamilton-Jacobi-Bellman equation in terms of directional derivatives has a solution consisting of the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem, and in specifying an optimal control policy in terms of the potential function. The results settle a hitherto open problem as well as generalize known results.

Hedging Options with Transaction Costs

This paper studies the optimal investment problem for an investor with a HARA type utility function. We assume the investor already has an option in her portfolio, and she will setup her invesment/hedging strategy using bonds and the underlying stock to maximize her utility. When there are transaction costs, the investor’s optimal investment/ hedging strategy can be described by three regions: the buying region, the selling region, and the no transaction region. When her portfolio falls in the buying (selling) region, she will buy (sell) enough shares of the stock to make her portfolio lie in the no transaction region (NT). When her portfolio falls in the NT region, it is optimal for the investor to make no transaction. We introduce the concept of a viscosity solution to describe the indirect utility function. A numerical scheme is proposed to compute the indirect utility function. This in turn enables the asking price for an option to be computed.

Producing in a manufacturing system with minimum average cost

We deal with a single or parallel machine manufacturing system with convex cost of holding and backlogging and develop a new rigorous analysis to address the problem. We provide the results needed for the vanishing discount approach used for aour analysis. In particular, we show that one can go from any point in the state space to any other point in a finite time. The Hamilton-Jacobi-Bellman (HJB) equation is specified for the average cost problem and a verification theorem for optimality over the class of admissible controls is given. We show that the HJB equation has a viscosity solution, which turns out in this case to be also a classical solution.