Portfolio Management Determined by Initial Endowment or Terminal Wealth in A Consumer Finance Market With Jumps

摘要

In the field of stochastic consumer finance market with jumps, we study portfolio and wealth processes decided by initial endowment or by initial and terminal wealth, as well as contingent claims and option valuation decided by terminal wealth. Comparing "deflator" with "discount factor", we give two kinds of proofs for each important theorem by stochastic analysis method. And we give the necessary sufficient conditions for the hedging strategies to duplicate completely the derivative securities contingent claims in markets, under the conditions of deterministic coefficients, using stochastic analysis and partial differential-difference equations.