Optimization, conservation and valuation of contingent claims in economic resource management under uncertainty Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/q811kn89s

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  • This dissertation consists of three papers studying optimization, conservation and valuation of contingent claims in economic resource nianagement under uncertainty. In the first paper the Markovian optinial policies are studied for resource management in a finite time horizon. Under sonic conditions, in particular, when the prices are stochastic and there is a positive fixed setup cost K, the existence of {S, .s}-type Markovian optimal management policies is proved. When K = 0, the optimal policies are of {S}-type, in which case a comparison is made between the optimal policies under stochastic and deterministic prices. It turns out that under stochastic prices the optimal policies should be more conservative in order to maximize the present value of expected revenue. The second paper investigates the issue of conservation under uncertainty of future benefits for both non-renewable and renewable resources. A framework is introduced to demonstrate that under uncertainty of future benefits the optimal management policy will be more conservative than the optimal policy obtained when the uncertainty is ignored. This paper extends early results by Arrow and Fisher (1974) for the case of irreversible management policies for non-renewable resources. In particular it is shown that resource conservation can be a consequence of profit maximization or timing of investments when future benefits are uncertain and the process of developing or harvesting is irreversible. In the third paper we discuss the valuation of contingent claims on economic resources. Contingent claims on certain economic resources may involve underlying assets with conversion costs or subsidies, in which case the price of underlying risky assets may be modeled by a geometric Brownian motion plus a deterministic conversion cost or subsidy. Under the circumstances, we derive the equation for valuing contingent claims on assets with conversion costs or subsidies and show that a unique arbitrage-free hedging strategy exists.
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