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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

The existence of a weak solution and the uniqueness in law are assumed for the equation, the coefficients b and σ being generally C ( + ) -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 ( + ) in the special case of a diffusion volatility σ ( X , t ) = σ ˜ ( X ( t ) ) . A martingale option pricing method is presented.

The martingale method of shortfall risk minimization in a discrete time market

Marek Andrzej Kociński (2012)

Applicationes Mathematicae

The shortfall risk minimization problem for the investor who hedges a contingent claim is studied. It is shown that in case the nonnegativity of the final wealth is not imposed, the optimal strategy in a finite market model is obtained by super-hedging a contingent claim connected with a martingale measure which is a solution of an auxiliary maximization problem.

The pricing of credit risky securities under stochastic interest rate model with default correlation

Anjiao Wang, Zhong Xing Ye (2013)

Applications of Mathematics

In this paper, we study the pricing of credit risky securities under a three-firms contagion model. The interacting default intensities not only depend on the defaults of other firms in the system, but also depend on the default-free interest rate which follows jump diffusion stochastic differential equation, which extends the previous three-firms models (see R. A. Jarrow and F. Yu (2001), S. Y. Leung and Y. K. Kwok (2005), A. Wang and Z. Ye (2011)). By using the method of change of measure and...

Thoughts about Selected Models for the Valuation of Real Options

Mikael Collan (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

This paper discusses option valuation logic and four selected methods for the valuation of real options in the light of their modeling choices. Two of the selected methods the Datar–Mathews method and the Fuzzy Pay-off Method represent later developments in real option valuation and the Black & Scholes formula and the Binomial model for option pricing the more established methods used in real option valuation. The goal of this paper is to understand the big picture of real option valuation models...

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