Wealth Process Sample Clauses

Wealth Process. Assume that investors can choose to invest their capital at both risky and riskless t assets. Let ui be the shares of investment in the ith asset at time t. Denote ut = (ut,2, ut,2, ..., —1)T as the vector of trading strategy through all assets. For liability u t Xx, we always assume holding —1 shares of it, i.e. ut,Li = —1. Let A denotes the total asset at time t under strategy ut. Then the wealth of total assets of holding at time t satisfies: t Xt = ψT ut. (3.35)

Wealth Process. Assuming that in the market, we have one riskless asset, one risky asset and nL lia- bilities. We denote ψt,1 as the riskless asset with interest rate µt,1 and random terms σt,1 = Yt,1 = 0; ψt,2 as the risky asset with appreciate rate µt,2 and volatility σt,2; ψt,Li as liability with appreciate rate µt,2 and volatility σt,2. The jump process of risky asset ψt,Li and liabilities ψt,Li are governed by Yt,2∆Nt and Yt,Li ∆Nt respectively. Denote ut = (ut,1, ut,2, —1, ..., —1)T as the shares of holding at time t. We further define wealth process Xt as the total assets minus total liabilities. In particular, for liabilities Li, we always assume ut,Li = —1. At any time t ∈ {0, ∆t, ..., T }, we can obtain the total wealth via t Xt = ψT ut. (4.5)