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Radically Elementary Probability Theory. (AM-117), Volume 117
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ISBN: 0691084734 0691084742 1400882141 Year: 2016 Publisher: Princeton, NJ : Princeton University Press,

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Abstract

Using only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.

Keywords

Martingales (Mathematics) --- Stochastic processes. --- Probabilities. --- Martingales (Mathematics). --- Stochastic processes --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Random processes --- Probabilities --- Abraham Robinson. --- Absolute value. --- Addition. --- Algebra of random variables. --- Almost surely. --- Axiom. --- Axiomatic system. --- Borel set. --- Bounded function. --- Cantor's diagonal argument. --- Cardinality. --- Cartesian product. --- Central limit theorem. --- Chebyshev's inequality. --- Compact space. --- Contradiction. --- Convergence of random variables. --- Corollary. --- Correlation coefficient. --- Counterexample. --- Dimension (vector space). --- Dimension. --- Division by zero. --- Elementary function. --- Estimation. --- Existential quantification. --- Family of sets. --- Finite set. --- Hyperplane. --- Idealization. --- Independence (probability theory). --- Indicator function. --- Infinitesimal. --- Internal set theory. --- Joint probability distribution. --- Law of large numbers. --- Linear function. --- Martingale (probability theory). --- Mathematical induction. --- Mathematician. --- Mathematics. --- Measure (mathematics). --- N0. --- Natural number. --- Non-standard analysis. --- Norm (mathematics). --- Orthogonal complement. --- Parameter. --- Path space. --- Predictable process. --- Probability distribution. --- Probability measure. --- Probability space. --- Probability theory. --- Probability. --- Product topology. --- Projection (linear algebra). --- Quadratic variation. --- Random variable. --- Real number. --- Requirement. --- Scientific notation. --- Sequence. --- Set (mathematics). --- Significant figures. --- Special case. --- Standard deviation. --- Statistical mechanics. --- Stochastic process. --- Subalgebra. --- Subset. --- Summation. --- Theorem. --- Theory. --- Total variation. --- Transfer principle. --- Transfinite number. --- Trigonometric functions. --- Upper and lower bounds. --- Variable (mathematics). --- Variance. --- Vector space. --- W0. --- Wiener process. --- Without loss of generality.


Book
Credit risk modeling : theory and applications
Author:
ISBN: 1282608010 9786612608018 1400829194 Year: 2004 Publisher: Princeton ; Oxford : Princeton University Press,

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"Credit risk is today one of the most intensely studied topics in quantitative finance. This book provides an introduction and overview for readers who seek an up-to-date reference to the central problems of the field and to the tools currently used to analyze them. The book is aimed at researchers and students in finance, at quantitative analysts in banks and other financial institutions, and at regulators interested in the modeling aspects of credit risk."--Jacket.

Keywords

Credit --- Management. --- Adapted process. --- Arbitrage. --- Asset Sales. --- Asset. --- Bankruptcy. --- Barrier option. --- Basis Point. --- Binomial approximation. --- Binomial distribution. --- Bond (finance). --- Bond Yield. --- Bond valuation. --- Calculation. --- Call option. --- Capital structure. --- Comparative advantage. --- Convenience yield. --- Coupon (bond). --- Coupon. --- Credit (finance). --- Credit default swap. --- Credit derivative. --- Credit rating. --- Credit risk. --- Credit spread (options). --- Cumulative Dividend. --- Current liability. --- Debt Issue. --- Debt. --- Discount function. --- Discrete time and continuous time. --- Dividend payout ratio. --- Dividend. --- Equity value. --- Equivalent Martingale Measures. --- Estimation. --- Estimator. --- Exponential distribution. --- Fair value. --- Geometric Brownian motion. --- Government bond. --- High-yield debt. --- Implicit cost. --- Implied volatility. --- Information asymmetry. --- Interest rate swap. --- Interest rate. --- Issuer. --- Jump process. --- Latent variable. --- Least squares. --- Leverage (finance). --- Liability (financial accounting). --- Libor. --- Logistic regression. --- Market liquidity. --- Market value. --- Markov chain. --- Markov model. --- Mathematical finance. --- Merton Model. --- Moment-generating function. --- Money market. --- Option (finance). --- Par Yield Curve. --- Path dependence. --- Payment. --- Plain vanilla. --- Predictable process. --- Present value. --- Pricing. --- Probability of default. --- Probability. --- Put option. --- Random variable. --- Recapitalization. --- Repurchase agreement. --- Risk management. --- Risk premium. --- Risk-neutral measure. --- Semimartingale. --- Short rate. --- State variable. --- Swap (finance). --- Swap Curve. --- Swap rate. --- Swap spread. --- Synthetic CDO. --- Tax advantage. --- Tax shield. --- Tax. --- Trading strategy. --- Tranche. --- Underlying Security. --- Value (economics). --- Variance. --- Vasicek model. --- Yield curve. --- Yield spread. --- Zero-coupon bond.

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