DATE: Thursday, March 22, 2007
LOCATION: E40-298
TIME: 4:15pm
Reception immediately following in the Philip M. Morse Reading Room, E40-106
ABSTRACT
In this talk I will present results from the paper on Hedging Inventory
Risk [1], as well as, some recent results on applications of the
valuation methodology proposed in that paper to an optimal inventory
timing problem [2].
In the first paper, we address the problem of hedging inventory
risk for a short lifecycle or seasonal item when its demand is
correlated with the price of a financial asset. We show how to
construct optimal hedging transactions that minimize the variance
of profit and increase the expected utility for a risk-averse decision-maker.
We show that for a wide range of hedging strategies and utility
functions, a risk-averse decision-maker orders more inventory when
he/she hedges the inventory risk. Our results are useful to both
risk-neutral and risk-averse decision-makers because: (1) The price
information of the financial asset is used to determine both the
optimal inventory level as well as the hedge. (2) This enables
the decision-maker to update the demand forecast and the financial
hedge as more information becomes available. (3) Hedging leads
to lower risk and higher return on inventory investment.
In the second paper, we consider a firm that faces the decision
of optimal timing of inventory investment when its forecasts of
demand and/or price improve with time but are correlated with prices
of portfolios in the financial market. We consider this problem
using a single period inventory model where demand is realized
at time T and the stocking decision may be made at any time in
the interval [0, T]. The firm is owned by risk-averse investors.
Thus, we use a risk-adjusted valuation approach for incomplete
markets to determine the optimal timing strategy.
We provide conditions under which postponement is always optimal
and conditions under which early exercise of the inventory option
takes place. We show the impact of risk-aversion and the volatilities
of price and demand on the optimal timing and stocking decisions.
Finally, we show how the procurement cost can be changed over time
to induce early exercise or postponement of the stocking decision.
We illustrate empirical insights from the model using data from
the gold mining industry.
[1] Gaur, V. and S. Seshadri, “Hedging Inventory Risk
Through Market Instruments,” Manufacturing and Service Operations
Management Journal, 7, 2, 2005, p. 103-120.
[2] Gaur, V., S. Seshadri, and M. Subrahmanyam, “Optimal
Timing of Inventory Decisions with Price Uncertainty,” working
paper, 2007.
