This thesis will look at three problems in financial mathematics. In the first, we seek to model the heterogeneous beliefs of agents in a dynamic economy. We study the class of models in which all agents receive the same stream of information. Their different beliefs about the system cause them to behave differently, yet still rationally. We explain how to determine the equilibrium and deduce the state price density for the agents; this enables us to (theoretically) calculate the price of any contingent claim. We look at three setups. The first is that in which all agents have logarithmic utility. We show how the model can explain observed phenomena such as rational overconfidence, speculation and volume of trade effects. The second setup introduces a continuum of finite-lived agents who learn about an unknown parameter of the output process of the single productive asset. Since the agents are finite-lived, they never discover the true value of the parameter and we can therefore determine a stationary solution. We also consider a third setup, in which the behaviour of the output process depends on a stochastic process that is not fully observed. The second problem is insurance pricing. We consider how prices behave when insurers do not know about the arrival rate and size of claims, as they have very little past data. We examine the amount of business received by each insurance company when they each charge different prices. We use this to determine the optimal price for each insurers to charge, given their perceived cost of providing insurance. Insurers are assumed to be Bayesian and so update their beliefs about the arrival rate and size of claims as they observe more data. This results in the perceiving cost of the insurance changing and the insurers adjusting their prices. The final topic looked at is the effect of market clearing on financial markets. We introduce a model with many CARA agents and many risky assets. We show that the market clearing condition can introduce correlation between assets whose dividend processes are independent.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:596999 |
| Date | January 2010 |
| Creators | Brown, A. A. |
| Publisher | University of Cambridge |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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