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  • 1.
    Canhanga, Betuel
    et al.
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Faculty of Sciences, Department of Mathematics and Computer Sciences, Eduardo Mondlane University, Maputo, Mozambique.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Ni, Ying
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Rancic, Milica
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Analytical and Numerical Studies on the Second Order Asymptotic Expansion Method for European Option Pricing under Two-factor Stochastic Volatilities2018In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 47, no 6, p. 1328-1349Article in journal (Refereed)
    Abstract [en]

    The celebrated Black–Scholes model made the assumption of constant volatility but empirical studies on implied volatility and asset dynamics motivated the use of stochastic volatilities. Christoffersen in 2009 showed that multi-factor stochastic volatilities models capture the asset dynamics more realistically. Fouque in 2012 used it to price European options. In 2013 Chiarella and Ziveyi considered Christoffersen's ideas and introduced an asset dynamics where the two volatilities of the Heston type act separately and independently on the asset price, and using Fourier transform for the asset price process and double Laplace transform for the two volatilities processes, solved a pricing problem for American options. This paper considers the Chiarella and Ziveyi model and parameterizes it so that the volatilities revert to the long-run-mean with reversion rates that mimic fast(for example daily) and slow(for example seasonal) random effects. Applying asymptotic expansion method presented by Fouque in 2012, we make an extensive and detailed derivation of the approximation prices for European options. We also present numerical studies on the behavior and accuracy of our first and the second order asymptotic expansion formulas.

  • 2.
    Ekheden, Erhard
    et al.
    Stockholm University.
    Silvestrov, Dmitrii
    Stockholm University.
    Coupling and explicit rates of convergence in Cramér-Lundberg approximation for          reinsurance risk processes2011In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 40, no 19-20, p. 3524-3539Article in journal (Refereed)
    Abstract [en]

    A classical result in risk theory is the Cramér-Lundberg approximation which says that under some general conditions the exponentially normalized ruin probability converges. In this article, we state an explicit rate of convergence for the Cramér-Lundberg approximation for ruin probabilities in the case where claims are bounded, which is realistic for, e.g., reinsurance models. The method, used to get the corresponding results, is based on renewal and coupling arguments.

  • 3.
    Silvestrov, D.
    et al.
    Stockholm University, Sweden.
    Manca, R.
    University of Rome La Sapienza, Rome, Italy .
    Silvestrova, Evelina
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Computational algorithms for moments of accumulated markov and semi-markov rewards2014In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 43, no 7, p. 1453-1469Article in journal (Refereed)
    Abstract [en]

    Power moments for accumulated rewards defined on Markov and semi-Markov chains are studied. A model with mixed time-space termination of reward accumulation is considered for inhomogeneous in time rewards and Markov chains. Characterization of power moments as minimal solutions of recurrence system of linear equations, sufficient conditions for finiteness of these moments and upper bounds for them, expressed in terms of so-called test functions, are given. Backward recurrence algorithms for funding of power moments of accumulated rewards and various time-space truncation approximations reducing dimension of the corresponding recurrence relations are described.

  • 4.
    Silvestrov, Dmitrii
    et al.
    Stockholm Univ., Sweden.
    Li, Y.
    Stockholm Univ., Sweden.
    Stochastic Approximation Methods for American Type Options2016In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 45, no 6, p. 1607-1631Article in journal (Refereed)
  • 5.
    Silvestrov, Dmitrii S.
    Mälardalen University, Department of Mathematics and Physics.
    Upper bounds for exponential moments of hitting times for semi-Markov processes2004In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 33, no 3, p. 533-543Article in journal (Other academic)
    Abstract [en]

    Necessary and sufficient conditions for the existence of exponential moments for hitting times for semi-Markov processes are found. These conditions and the corresponding upper bounds for exponential moments are given in terms of test-functions. Applications to hitting times for semi-Markov random walks and queuing systems illustrate the results.

  • 6.
    Silvestrov, Dmitrii S.
    Mälardalen University, Department of Mathematics and Physics.
    Upper bounds for exponential moments of hitting times for semi-Markov processes2004In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 33, no 3, p. 533-544Article in journal (Refereed)
    Abstract [en]

    Necessary and sufficient conditions for the existence of exponential moments for hitting times for semi-Markov processes are found. These conditions and the corresponding upper bounds for exponential moments are given in terms of test-functions. Applications to hitting times forsemi-Markov random walks and queuing systems illustrate the results.

  • 7.
    Silvestrov, Dmitrii
    et al.
    Mälardalen University, Department of Mathematics and Physics.
    Stenberg, Fredrik
    Mälardalen University, Department of Mathematics and Physics.
    A pricing process with stochastic volatility controlled by a semi-Markov process2004In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 33, no 3, p. 591-608Article in journal (Refereed)
    Abstract [sv]

    This paper is devoted to the investigation of the geometrical Brownian motion as a price process where the drift and volatility are controlled by a semi-Markov process. Conditions of risk-neutral measure are given as well as a formula for the risk-neutral price for European options. The discrete version, the binomial model controlled by a semi-Markov chain, is examined and limit theorems describing the transition from discrete time binomial to continuous time model are given. A system of partial differential equations for distribution functions of average volatility is given. Related Monte Carlo algorithms are described.

1 - 7 of 7
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