Chapter 8: Utility indifference pricing and dynamic programming algorithm

Contents Utility indifference pricing Dynamic programming A general pricing framework beyond the Black-Scholes world, where perfect replication is impossible. Optimal control problems are involved Dynamic programming A numerical method for (continuous-time) optimal control problems The simplest example is the binomial tree method for American options

Utility indifference: from the angle of an option’s writer

The target of the writer

Indifference price

Indifference price with exponential utility In the Black-Scholes market, the indifference price reduces to the Black-Scholes price. The price is non-linear in the number of options.

Pricing in discrete time

Dynamic programming

First order condition

An example: jump-diffusion market

Quadrinomial tree

Pseudo code (J=3)

Numerical results