Wealth Process Sample Clauses

Wealth Process. Assume that investors can choose to invest their capital at both risky and riskless 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 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: 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 Xt = ψT ut. (4.5) 4.3 Mean Variance Optimisation Problem