Malliavin calculus in Lev́y spaces and applications to finance.
Malliavin method for optimal investment in financial markets with memory
We consider a financial market with memory effects in which wealth processes are driven by mean-field stochastic Volterra equations. In this financial market, the classical dynamic programming method can not be used to study the optimal investment problem, because the solution of mean-field stochastic Volterra equation is not a Markov process. In this paper, a new method through Malliavin calculus introduced in [1], can be used to obtain the optimal investment in a Volterra type financial market....
Martingales and arbitrage: a new look.
Matematické modely oceňování amerických kupních opcí
Mathematical methods in modern risk measurement: a survey.
Mean variance and goal achieving portfolio for discrete-time market with currently observable source of correlations
The paper studies optimal portfolio selection for discrete time market models in mean-variance and goal achieving setting. The optimal strategies are obtained for models with an observed process that causes serial correlations of price changes. The optimal strategies are found to be myopic for the goal-achieving problem and quasi-myopic for the mean variance portfolio.
Measuring of second–order stochastic dominance portfolio efficiency
In this paper, we deal with second-order stochastic dominance (SSD) portfolio efficiency with respect to all portfolios that can be created from a considered set of assets. Assuming scenario approach for distribution of returns several SSD portfolio efficiency tests were proposed. We introduce a -SSD portfolio efficiency approach and we analyze the stability of SSD portfolio efficiency and -SSD portfolio efficiency classification with respect to changes in scenarios of returns. We propose new...
Mixing conditions for multivariate infinitely divisible processes with an application to mixed moving averages and the supOU stochastic volatility model
We consider strictly stationary infinitely divisible processes and first extend the mixing conditions given in Maruyama [Theory Probab. Appl. 15 (1970) 1–22] and Rosiński and Żak [Stoc. Proc. Appl. 61 (1996) 277–288] from the univariate to the d-dimensional case. Thereafter, we show that multivariate Lévy-driven mixed moving average processes satisfy these conditions and hence a wide range of well-known processes such as superpositions of Ornstein − Uhlenbeck (supOU) processes or (fractionally integrated)...
Modeling and pricing of variance and volatility swaps for local semi-Markov volatilities in financial engineering.
Modelling consumer credit risk via survival analysis.
Modelling financial time series using reflections of copulas
We have intensified studies of reflections of copulas (that we introduced recently in [6]) and found that their convex combinations exhibit potentially useful fitting properties for original copulas of the Normal, Frank, Clayton and Gumbel types. We show that these properties enable us to construct interesting models for the relations between investment in stocks and gold.
Modelling Real World Using Stochastic Processes and Filtration
First we give an implementation in Mizar [2] basic important definitions of stochastic finance, i.e. filtration ([9], pp. 183 and 185), adapted stochastic process ([9], p. 185) and predictable stochastic process ([6], p. 224). Second we give some concrete formalization and verification to real world examples. In article [8] we started to define random variables for a similar presentation to the book [6]. Here we continue this study. Next we define the stochastic process. For further definitions...
Modified neural network algorithms for predicting trading signals of stock market indices.
More multiplicity
More Multiplicity in the Rate of Interest; Poly-party and Poly-creditor Transactions. II
More Multiplicity in the Rate of Interest; Poly-party and Poly-creditor Transactions. I
Multivariate extensions of expectiles risk measures
This paper is devoted to the introduction and study of a new family of multivariate elicitable risk measures. We call the obtained vector-valued measures multivariate expectiles. We present the different approaches used to construct our measures. We discuss the coherence properties of these multivariate expectiles. Furthermore, we propose a stochastic approximation tool of these risk measures.