Essays on inventory, pricing and financial trading strategies

Abstract

In a multi-product market, if one product stocks out, consumers may substitute to competing products. In this thesis, we use an axiomatic approach to characterize a price-dependent demand substitution rule, and provide a sufficient and necessary condition for demand models where our demand substitution rule applies. Our results can serve as a link between the pricing and inventory literature, and enable the study of joint pricing and inventory coordination and competition. I demonstrate the impact of this axiomatic approach on the joint pricing and inventory coordination model by incorporating the price-dependent demand substitution rule, and illustrate that if the axiomatic approach is acceptable, the optimal strategy and corresponding expected profit are quite different than models that ignore stockout demand substitution. I use this price-dependent demand substitution rule to model the joint pricing and inventory game, and study the existence of Nash equilibrium in this game. In the second part of this thesis, I consider the problem of dynamically trading a security over a finite time horizon. The model assumes that a trader has a "safe price" for the security, which is the highest price that the trader is willing to pay for this security in each time period. A trader's order has both temporary (short term) and permanent (long term) impact on the security price and the security price may increase after the trader's order, to a point where it is above the safe price. Given a safe price constraint for the current time period, I characterize the optimal policy for the trader to maximize the total number of securities he can buy over a fixed time horizon.

(cont.) In particular, I consider a greedy policy, which involves at each stage buying a quantity that drives the temporary price to the security safety price. I show that the greedy policy is not always optimal and provide conditions under which the greedy policy is optimal. I also provide bounds on the performance of the greedy policy relative to the performance of the optimal policy.