Displaying similar documents to “Exponential martingales and CIR model”

Optimal stopping of a 2-vector risk process

Krzysztof Szajowski (2010)

Banach Center Publications

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The following problem in risk theory is considered. An insurance company, endowed with an initial capital a > 0, receives insurance premiums and pays out successive claims from two kind of risks. The losses occur according to a marked point process. At any time the company may broaden or narrow down the offer, which entails the change of the parameters of the underlying risk process. These changes concern the rate of income, the intensity of the renewal process and the distribution...

Tail asymptotics for exponential functionals of Lévy processes: The convolution equivalent case

Víctor Rivero (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We determine the rate of decrease of the right tail distribution of the exponential functional of a Lévy process with a convolution equivalent Lévy measure. Our main result establishes that it decreases as the right tail of the image under the exponential function of the Lévy measure of the underlying Lévy process. The method of proof relies on fluctuation theory of Lévy processes and an explicit pathwise representation of the exponential functional as the exponential functional of a...

An explicit solution for optimal investment problems with autoregressive prices and exponential utility

Sándor Deák, Miklós Rásonyi (2015)

Applicationes Mathematicae

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We calculate explicitly the optimal strategy for an investor with exponential utility function when the price of a single risky asset (stock) follows a discrete-time autoregressive Gaussian process. We also calculate its performance and analyse it when the trading horizon tends to infinity. Dependence of the asymptotic performance on the autoregression parameter is determined. This provides, to the best of our knowledge, the first instance of a theorem linking directly the memory of...

Bayes sequential estimation procedures for exponential-type processes

Ryszard Magiera (1994)

Applicationes Mathematicae

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The Bayesian sequential estimation problem for an exponential family of processes is considered. Using a weighted square error loss and observing cost involving a linear function of the process, the Bayes sequential procedures are derived.

Discrete-time market models from the small investor point of view and the first fundamental-type theorem

Marek Karaś, Anna Serwatka (2017)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this paper, we discuss the no-arbitrage condition in a discrete financial market model which does not hold the same interest rate assumptions. Our research was based on, essentially, one of the most important results in mathematical finance, called the Fundamental Theorem of Asset Pricing. For the standard approach a risk-free bank account process is used as numeraire. In those models it is assumed that the interest rates for borrowing and saving money are the same. In our paper we...

The d X ( t ) = X b ( X ) d t + X σ ( X ) d W equation and financial mathematics. I

Josef Štěpán, Petr Dostál (2003)

Kybernetika

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The existence of a weak solution and the uniqueness in law are assumed for the equation, the coefficients b and σ being generally C ( ℝ + ) -progressive processes. Any weak solution X is called a ( b , σ ) -stock price and Girsanov Theorem jointly with the DDS Theorem on time changed martingales are applied to establish the probability distribution μ σ of X in C ( ℝ + ) in the special case of a diffusion volatility σ ( X , t ) = σ ˜ ( X ( t ) ) . A martingale option pricing method is presented.