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Journal of Computational and Applied Mathematics, ISSN 0377-0427, 10/2015, Volume 287, pp. 63 - 66
We propose numerical integration methods for Choquet integrals where the capacities are given by distortion functions of an underlying probability measure. It... 
Quasi-Monte Carlo methods | Risk measures | Choquet integrals | MATHEMATICS, APPLIED | RISK | Monte Carlo method | Methods | Monte Carlo methods | Approximation | Integrals | Mathematical analysis | Distortion | Mathematical models | Continuity | Representations
Journal Article
Japan Journal of Industrial and Applied Mathematics, ISSN 0916-7005, 11/2014, Volume 31, Issue 3, pp. 681 - 696
... in continuous time Yumiharu Nakano Received: 22 January 2013 / Revised: 4 October 2014 / Published online: 18 October 2014 © The JJIAM Publishing Committee and Springer... 
Computational Mathematics and Numerical Analysis | Monte Carlo methods | 93E20 | Mathematics | Applications of Mathematics | Stochastic controls | Kernel density estimation | Hamilton–Jacobi–Bellman equations | Viscosity solutions | 49M99 | MATHEMATICS, APPLIED | CONVERGENCE | Hamilton-Jacobi-Bellman equations | SIMULATION | Markov processes | Monte Carlo method
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2004, Volume 293, Issue 1, pp. 345 - 354
The idea of efficient hedging has been introduced by Föllmer and Leukert. They defined the shortfall risk as the expectation of the shortfall weighted by a... 
Worst conditional expectation | Efficient hedging | Hedging | Randomized test | Shortfall risk | Coherent risk measure | Neyman–Pearson lemma | Neyman-Pearson lemma | efficient hedging | MATHEMATICS | hedging | MATHEMATICS, APPLIED | shortfall risk | worst conditional expectation | coherent risk measure | randomized test
Journal Article
Journal of mathematical finance, ISSN 2162-2434, 2015, Volume 5, Issue 2, pp. 113 - 115
Journal Article
Stochastic partial differential equations : analysis and computations, ISSN 2194-0401, 03/2020, Volume 8, Issue 1, pp. 262 - 263
Journal Article
05/2020
We study an inverse problem of the stochastic control of general diffusions with performance index having the quadratic penalty term of the control process.... 
Mathematics - Optimization and Control
Journal Article
Automatica, ISSN 0005-1098, 04/2016, Volume 66, pp. 205 - 217
Journal Article
03/2018
We prove that the functions constructed by the kernel-based regressions with Wendland kernels under $\ell_1$-norm constraints converge to unique viscosity... 
Journal Article
Numerische Mathematik, ISSN 0029-599X, 07/2017, Volume 136, Issue 3, pp. 703 - 723
We prove the convergence of meshfree collocation methods for the terminal value problems of fully nonlinear parabolic partial differential equations in the... 
65M70 | 35K55 | MATHEMATICS, APPLIED | APPROXIMATION SCHEME
Journal Article
10/2017
We examine an application of the kernel-based interpolation to numerical solutions for Zakai equations in nonlinear filtering, and aim to prove its rigorous... 
Journal Article
Stochastics and Partial Differential Equations: Analysis and Computations, ISSN 2194-0401, 9/2019, Volume 7, Issue 3, pp. 476 - 494
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 2004, Volume 67, Issue 1, pp. 87 - 95
In a jump-diffusion model of complete financial markets, we study the problem of minimizing the expectation of hedging loss weighted by power functions. We... 
Jump-diffusion model | Shortfall risk | shortfall risk | STATISTICS & PROBABILITY | jump-diffusion model | Shortfall risk Jump-diffusion model
Journal Article
01/2016
This note presents a kind of the strong law of large numbers for an insurance risk caused by a single catastrophic event rather than by an accumulation of... 
Quantitative Finance - Risk Management
Journal Article
09/2018
We propose kernel-based collocation methods for numerical solutions to Heath-Jarrow-Morton models with Musiela parametrization. The methods can be seen as the... 
Journal Article
11/2014
We propose numerical integration methods for Choquet integrals where the capacities are given by distortion functions of an underlying probability measure. It... 
Mathematics - Numerical Analysis
Journal Article
08/2014
We prove the convergence of meshfree collocation methods for the terminal value problems of fully nonlinear parabolic partial differential equations in the... 
Mathematics - Numerical Analysis
Journal Article
Journal of mathematical finance, ISSN 2162-2434, 2013, Volume 3, Issue 3, pp. 392 - 400
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 2007, Volume 77, Issue 3, pp. 256 - 264
We construct a binary market model with memory that approximates a continuous-time market model driven by a Gaussian process equivalent to Brownian motion. We... 
Arbitrage | Financial market with memory | Binary market | FINANCIAL-MARKETS | STATISTICS & PROBABILITY | binary market | arbitrage | financial market with memory | Financial market with memory Binary market Arbitrage
Journal Article
ASTIN bulletin, ISSN 0515-0361, 05/2012, Volume 42, Issue 1, pp. 343 - 353
The optimal quantization theory is applied for approximating law-invariant comonotonic coherent risk measures. Simple Lp -norm estimates for the risk measures... 
Coherent risk measures | Comonotonicity | Average value-at-risk | Optimal quantization | average value-at-risk | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | optimal quantization | comonotonicity | STATISTICS & PROBABILITY | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS
Journal Article
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