Applications of dynamic optimization to strategic pricing and corporate finance

This thesis consists of four essays that utilize various methods of dynamic optimization to solve problems in strategic pricing and corporate finance. In the first part of the thesis, we develop dynamic pricing models for consumer products, taking into consideration the strategic behavior of customers. In the second paxt, we develop models that characterize the optimal decisions for management of liquidity and investment opportunities of corporations.; In contrast to the traditional pricing models where customers are assumed to base their decisions solely on the current information (e.g., prices and inventory levels), strategic pricing models take into consideration the fact that customers maybe using information from the past, and/or their anticipation of the future, in their decision making. In Chapter 2, we study the behavior of a strategic customer who times her purchase to minimize the expected cost. We consider industries where the product acquisition time has little or no impact on the customer's utility. Examples include the airline and the hotel industries, where tickets and rooms can be purchased at any time before the travel date. We use dynamic programming to solve for an optimal purchasing policy for customers, and subsequently for an optimal pricing policy in response to this behavior. In Chapter 3, we consider customers who use historical prices, instead of future prices, to aid their decisions. Customers form a reference price of a product from their past experiences. Any discount (surcharge) over the reference price will have a positive (negative) impact on customer's utility and demand. This type of behavior is common for industries where products are repeatedly sold to the same population of customers over time. We extend the concept of product-level reference price to store-level reference price, and solve for optimal pricing policies of multiple products in monopoly and duopoly markets.; In the second part of the thesis, we develop structural models that address corporate finance issues such as liquidity management, dividend policy and investment policy. To capture the effect of frictions in the capital market, we use the concept of costly equity dilution, which is largely missing from the literature on corporate debt valuation. In Chapter 4, we investigate three methods of managing illiquidity: equity dilution, maintaining cash reserves, and entering into loan commitment agreements. We study the impact of costly equity dilution on security prices and optimal capital structure. We show that maintaining a cash reserve is generally less efficient than signing on a loan commitment contract. We completely characterize the optimal strategy of both methods, in terms of an optimal dividend policy, and an optimal draw/repayment of the loan commitment. In Chapter 5, we develop a structural model that captures the interaction between cash and investment opportunities. In our model, the firm optimally balances the pay out of dividends with the buildup of a cash reserve, either to finance growth opportunities in good states, or to provide liquidity in bad states. We provide a complete characterization of the firm's strategy in terms of its investment and dividend policy.