A combined Monte Carlo and quasi-Monte Carlo method with applications to option pricing.
A comparative analysis of the value of information in a continuous time market model with partial information: the cases of log-utility and CRRA.
A few evaluation criteria of optimum financing with random costs and benefits.
A fuzzy approach to option pricing in a Levy process setting
In this paper the problem of European option valuation in a Levy process setting is analysed. In our model the underlying asset follows a geometric Levy process. The jump part of the log-price process, which is a linear combination of Poisson processes, describes upward and downward jumps in price. The proposed pricing method is based on stochastic analysis and the theory of fuzzy sets. We assume that some parameters of the financial instrument cannot be precisely described and therefore they are...
A general version of the fundamental theorem of asset pricing.
A lot-size model for deteriorating items under conditions of a one-time only extended credit period.
A Markov regime-switching marked point process for short-rate analysis with credit risk.
A martingale control variate method for option pricing with stochastic volatility
A generic control variate method is proposed to price options under stochastic volatility models by Monte Carlo simulations. This method provides a constructive way to select control variates which are martingales in order to reduce the variance of unbiased option price estimators. We apply a singular and regular perturbation analysis to characterize the variance reduced by martingale control variates. This variance analysis is done in the regime where time scales of associated driving volatility...
A natural characterization of nonlinear cost rules
We prove a new characterization of cost rules based on the relationship between the classes of unambiguous and nonwasteful assets in incomplete frictionless markets.
A new decision-making method for stock portfolio selection based on computing with linguistic assessment.
A note on extremality and completeness in financial markets with infinitely many risky assets
A note on -balayages of matrix-exponential Lev́y processes.
A note on stochastic integration with respect to optional semimartingales.
A note on the optimal portfolio problem in discrete processes
We deal with the optimal portfolio problem in discrete-time setting. Employing the discrete Itô formula, which is developed by Fujita, we establish the discrete Hamilton–Jacobi–Bellman (d-HJB) equation for the value function. Simple examples of the d-HJB equation are also discussed.
A priori error estimates for reduced order models in finance
Mathematical models for option pricing often result in partial differential equations. Recent enhancements are models driven by Lévy processes, which lead to a partial differential equation with an additional integral term. In the context of model calibration, these partial integro differential equations need to be solved quite frequently. To reduce the computational cost the implementation of a reduced order model has shown to be very successful numerically. In this paper we give a priori error...
A probability density function estimation using F-transform
The aim of this paper is to propose a new approach to probability density function (PDF) estimation which is based on the fuzzy transform (F-transform) introduced by Perfilieva in [10]. Firstly, a smoothing filter based on the combination of the discrete direct and continuous inverse F-transform is introduced and some of the basic properties are investigated. Next, an alternative approach to PDF estimation based on the proposed smoothing filter is established and compared with the most used method...
A recursive robust Bayesian estimation in partially observed financial market
I propose a nonlinear Bayesian methodology to estimate the latent states which are partially observed in financial market. The distinguishable character of my methodology is that the recursive Bayesian estimation can be represented by some deterministic partial differential equation (PDE) (or evolution equation in the general case) parameterized by the underlying observation path. Unlike the traditional stochastic filtering equation, this dynamical representation is continuously dependent on the...
A reduced modelling approach to the pricing of mortgage backed securities.
A stochastic programming approach to managing liquid asset portfolios
Maintaining liquid asset portfolios involves a high carry cost and is mandatory by law for most financial institutions. Taking this into account a financial institution's aim is to manage a liquid asset portfolio in an “optimal” way, such that it keeps the minimum required liquid assets to comply with regulations. In this paper we propose a multi-stage dynamic stochastic programming model for liquid asset portfolio management. The model allows for portfolio rebalancing decisions over a multi-period...
A theoretical argument why the -copula explains credit risk contagion better than the Gaussian copula.