hw5 (2) - PDE for Finance, Spring 2011 Homework 5...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PDE for Finance, Spring 2011 Homework 5 Distributed 4/4/11, due 4/18/11 . Problem 1 is a classic example (due to Merton) of optimal asset allocation. Problems 2-4 reinforce our discussion of optimal stopping and American options. 1) Consider the following asset-allocation problem. Two investment opportunities are avail- able. One is risk-free, earning (constant) interest r . The other is lognormal, with (constant) drift and volatility , i.e. it satisfies dp = pds + pdw . You start at time t by investing wealth x . Your control is the weighting of your portofolio between these two assets, i.e. ( s ) = fraction of wealth invested in the risky asset at time s subject to 0 1. You never withdraw from or add to the portfolio, and you have a fixed horizon T . Your goal is to maximize the utility of your portfolio value at time T ; in other words, your value function is u ( x,t ) = max ( s ) E y ( t )= x [ h ( y ( T ))] where y ( s ) is the value of the portfolio at time...
View Full Document

Page1 / 2

hw5 (2) - PDE for Finance, Spring 2011 Homework 5...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online