## Stochastic Analysis, Stochastic Systems, and Applications to FinanceAllanus Hak-Man Tsoi, David Nualart, George Yin This book introduces some advanced topics in probability theories OCo both pure and applied OCo is divided into two parts. The first part deals with the analysis of stochastic dynamical systems, in terms of Gaussian processes, white noise theory, and diffusion processes. The second part of the book discusses some up-to-date applications of optimization theories, martingale measure theories, reliability theories, stochastic filtering theories and stochastic algorithms towards mathematical finance issues such as option pricing and hedging, bond market analysis, volatility studies and asset trading modeling. |

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apply approximate asset price assume Bayes estimates Björk bond market bond price bounded cash flow process condition consider continuous-time convergence counting process defined denote Department of Mathematics exponential exponential utility failure time data filtering equation follower's formulation fractional Brownian motion Gaussian process geometric Brownian motion given incomplete markets inf{t investment jump Ker(V leader Lemma local martingale Markov chain martingale measure Mathematical Finance mean-variance hedging minimal entropy martingale observed optimal stopping option pricing paper parameters payoff portfolio posterior predictable process probability problem Proof random recursive algorithm regime regime-switching model regression reinsurance satisfying Section semimartingale simulation solution stock prices strategy survival analysis Theorem threshold values trading value function variables volatility wealth process white noise Zºº