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- Eckhard Platen
- 2000

The paper introduces an approach for the derivation of discrete time approximations for solutions of stochastic di erential equations with time delay. The suggested approximations converge in a strong sense. Furthermore, explicit solutions for linear stochastic delay equations are given.

This paper proposes a new explanation for the smile and skewness effects in implied volatilities. Starting from a microeconomic equilibrium approach, we develop a diffusion model for stock prices explicitly incorporating the technical demand induced by hedging strategies. This leads to a stochastic volatility endogenously determined by agents’ trading… (More)

The paper proposes the use of the growth optimal portfolio for pricing and hedging in incomplete markets when there are unobserved factors that have to be filtered. The proposed filtering framework is applicable also in cases when there does not exist an equivalent risk neutral martingale measure. The reduction of the variance of derivative prices for… (More)

- Eckhard Platen
- 2003

This paper considers a diversified world stock index in a continuous financial market with the growth optimal portfolio (GOP) as the reference unit or benchmark. Diversified broadly based portfolios, which include major world stock market indices, are shown to approximate the GOP. It is demonstrated that a key financial quantity is the drift of the… (More)

- Eckhard Platen, Jason West
- 2004

This paper proposes a consistent approach to the pricing of weather derivatives. Since weather derivatives are traded in an incomplete market setting, standard hedging based pricing methods cannot be applied. The growth optimal portfolio, which is interpreted as a world stock index, is used as a benchmark or numeraire such that all benchmarked derivative… (More)

This paper introduces a new estimation technique for discretely observed diffusion processes. Transform functions are applied to transform the data to obtain good and easily calculated estimators of both the drift and diffusion coefficients. Consistency and asymptotic normality of the resulting estimators is investigated. Power transforms are used to… (More)

- Eckhard Platen
- 2003

The paper describes a general framework for contingent claim valuation for finance, insurance and general risk management. It considers security prices and portfolios with finite expected returns, where the growth optimal portfolio is taken as numeraire or benchmark. Benchmarked nonnegative wealth processes are shown to be supermartingales. Fair benchmarked… (More)

This paper proposes a consistent approach to discrete time valuation in insurance and finance. This approach uses the growth optimal portfolio as reference unit or benchmark. When used as benchmark, it is shown that all benchmarked price processes are supermartingales. Benchmarked fair price processes are characterized as martingales. No measure… (More)

- Leunglung Chan, Eckhard Platen
- J. Computational Applied Mathematics
- 2015

- Eckhard Platen, Renata Rendek
- 2009

Abstract. This paper studies the application of exact simulation methods for multi-dimensional multiplicative noise stochastic differential equations to filtering. Stochastic differential equations with multiplicative noise naturally occur as Zakai equation in hidden Markov chain filtering. The paper proposes a quasi-exact approximation method for hidden… (More)