Knut K. Aase

White Noise Generalizations of the Clark-Haussmann-Ocone Theorem with Application to Mathematical Finance

Abstract. We use a white noise approach to Malliavin calculus to prove the following white noise generalization of the Clark-Haussmann-Ocone formula \[F(\omega)=E[F]+\int_0^TE[D_tF|\F_t]\diamond W(t)dt\] Here E[F] denotes the generalized expectation,

Pricing of Unit-linked Life Insurance Policies

D_tF(\omega)={{dF}\over{d\omega}}

Contingent claims valuation when the security price is a combination of an Ito process and a random point process

is the (generalized) Malliavin derivative,

Optimum portfolio diversification in a general continuous-time model

\diamond

An Equilibrium Model of Catastrophe Insurance Futures and Spreads

is the Wick product and W(t) is 1-dimensional Gaussian white noise. The formula holds for all

EQUILIBRIUM IN A REINSURANCE SYNDICATE; EXISTENCE, UNIQUENESS AND CHARACTERIZATION

f\in{\cal G}^*\supset L^2(\mu)

Using the Donsker Delta Function to Compute Hedging Strategies

, where

Dynamic Equilibrium and the Structure of Premiums in a Reinsurance Market

{\cal G}^*

A MARKOV MODEL FOR THE PRICING OF CATASTROPHE INSURANCE FUTURES AND SPREADS

is a space of stochastic distributions and

Equilibrium Pricing in the Presence of Cumulative Dividends Following a Diffusion

\mu