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Bimodality testing of the stochastic cusp model
Voříšek, Jan
Multimodal distributions are popular in many areas: biology (fish and shark population), engineering (material collapse under pressure, stability of ships), psychology (attitude transitions), physics (freezing of water) etc. There were a few attempts to utilize multimodal distributions in financial mathematics as well. Cobb et al. described a class of multimodal distributions belonging to the exponential family, which has unique maximum likelihood estimators and showed a connection to the stationary distribution of the stochastic cusp catastrophe model. Moreover was shown, how to identify bimodality for given parameters of the stochastic cusp model using the sign of Cardans discriminant. A statistical test for bimodality of the stochastic cusp model using maximum likelihood estimates is proposed in the paper as well as the necessary condition for bimodality which can be used for s simplified testing to reject bimodality. By proposed methods is tested the bimodality of exchange rate between USD and GBP in the periods within the years 1975 - 2014.
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Scenario Generation via L-1 Norm
Kaňková, Vlasta
Optimization problems depending on a probability measure correspond to many economic and financial situations. It can be very complicated to solve these problems, especially when the underlying probability measure belongs to continuous type. Consequently, the underlying continuous probability measure is often replaced by discrete one with finite number of atoms (scenario). The aim of the contribution is to deal with the above mentioned approximation in a special form of stochastic optimization problems with an operator of the mathematical expectation in the objective function. The stability results determined by the help of the Wasserstein metric (based on the L_1 norm) are employed to generate approximate distributions
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Second Order Optimality in Transient and Discounted Markov Decision Chains
Sladký, Karel
The article is devoted to second order optimality in Markov decision processes. Attention is primarily focused on the reward variance for discounted models and undiscounted transient models (i.e. where the spectral radius of the transition probability matrix is less than unity). Considering the second order optimality criteria means that in the class of policies maximizing (or minimizing) total expected discounted reward (or undiscounted reward for the transient model) we choose the policy minimizing the total variance. Explicit formulae for calculating the variances for transient and discounted models are reported along with sketches of algoritmic procedures for finding second order optimal policies.
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Statistical analysis of competing risks in an unemployment study
Volf, Petr
This study is concerned with the analysis of dependence of random variables - latent times to events, in a competing risks case. We discuss first the problem of identifiability of marginal and joint distributions of competing random variables. Then, the copula models are utilized in order to express the dependence. Finally, the Gauss copula is used to solution of a real example with unemployment data.
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