Stochastic Finance, 4th Edition

4.8Measures of risk in a financial market

In this section, we will consider risk measures which arise in the financial market model of Section 1.1. In this model, d + 1 assets are priced at times t = 0 and t = 1. Prices at time 1 are modeled as nonnegative random variables S0, S1, . . . , Sd on some probability space (Ω,F, P), with S0 ≡ 1 + r. Prices at time 0 are given by a vector = (1, π), with π = (π1, . . . , πd). The discounted net gain of a trading strategy = (ξ0, ξ) is given by ξ · Y, where the random vector Y = (Y1, . . . , Yd) is defined ...