WOLFRAM|DEMONSTRATIONS PROJECT

Terminal Wealth Optimization with Power and Log Utility

​
view
utility function
optimal trading strategy
expected portfolio value
investment parameters
risk aversion β
0
time horizon T
1
initial endowment x
100
model parameters
stock return α
0.1
interest rate r
0.05
volatility σ
0.2
additional jump parameters
jump intensity λ
0.1
jump size γ
-0.05
diffusion
jump diffusion
optimal strategy π:
1.25
1.12
expected terminal wealth V(T):
111.91
110.55
optimal performance Φ(x):
4.69
4.68
This Demonstration shows the optimal solution to the problem of maximizing the expected utility from terminal wealth. You can choose between power utility and logarithmic utility. It is assumed that there are only two assets in the market, a riskless bond and a stock that follows a geometric Brownian motion (Black–Scholes model). Additionally, you can choose to introduce simple jumps to the stock model. The jumps are given by a compound Poisson process.