A benchmark approach to finance
This paper derives a unified framework for portfolio optimization, derivative pricing,financial modeling, and risk measurement. It is based on the natural assumption thatinvestors prefer more rather than less, in the sense that given two portfolios with thesame diffusion coefficient value, the one with the higher drift is preferred. Each suchinvestor is shown to hold an efficient portfolio in the sense of Markowitz with unitsin the market portfolio and the savings account. The market portfolio of investablewealth is shown to equal a combination of the growth optimal portfolio (GOP) andthe savings account. Tnthis setup the capital asset pricing model follows without the useof expected utility functions, Markovianity, or equilibrium assumptions. The expectedincrease of the discounted value of the GOP is shown to coincide with the expectedincrease of its discounted underlying value. The discounted GOP has the dynamics ofa time transformed squared Bessel process of dimension four. The time transformationis given by the discounted underlying value of the GOP. The squared volatility of theGOP equals the discounted GOP drift, when expressed in units of the discounted GOP.Riskneutral derivative pricing and actuarial pricing are generalized by the fair pricingconcept, which uses the GOP as numeraire and the realworld probability measure aspricing measure. An equivalent riskneutral martingale measure does not exist underthe derived minimal market model.
Year of publication: 
2005


Authors:  Platen Eckhard 
Publisher: 
Blackwell Publishing Asia 
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