1. Chapter 8: Utility indifference pricing and dynamic programming algorithm

2. 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

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

4. The target of the writer

5. Indifference price

6. 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.

7. Pricing in discrete time

8. Dynamic programming

9. First order condition

10. An example: jump-diffusion market

11. Quadrinomial tree

12. Pseudo code (J=3)

13. Numerical results