## Mathematical Modelling and Numerical Methods in Finance: Special VolumeMathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains.• Coverage of all aspects of quantitative finance including models, computational methods and applications • Provides an overview of new ideas and results • Contributors are leaders of the field |

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Alain Bensoussan algorithm American option American option price approximation arbitrage assume assumption barrier options Black–Scholes boundary bounded Brownian motion call option compute condition consider constant convex defined denote derivative differential equations discrete downside drawdown dynamic error estimates European option example Financ finite Föllmer formula geometric Brownian motion given grid horizon integral investment jump Karatzas LEMMA Lévy process linear lookback Luschgy Malliavin Malliavin calculus martingale Math Mathematical matrix mesh method Monte Carlo numerical observation obtain optimal quantization Pagès parameters payoff function portfolio probability measure problem product quantization PROOF PUM strategy put option quadratic respect risk constraints risk measures robust utility satisfies Schied Section simulation solution space sparse grid Stoch stochastic differential equations stochastic process stochastic volatility supermartingale Theorem utility maximization problem variance vector