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Numerical Method (3): PDE Approach*
Feynman–Kac theorem shows the equivalence of an expectation calculation and the solution to the related PDE for option pricing. In this chapter, we...
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On a Flexible Loan Repayment Method Depending on Borrower’s Asset with an Early Termination Clause
Aiming at the problem that the asset’s fluctuation influences the borrower’s repayment ability, a loan with a new and flexible repayment method is...
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Preliminary Mathematical Theory
In this chapter, we collect some basic mathematical theorems and concepts which will be useful in later chapters. Of course, it is impossible to...
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Climate Risk in Structural Credit Models
This survey article reviews the current state of literature on how structural models of credit risk are employed to model the impact of climate risk...
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DG Method for Pricing European Options under Merton Jump-Diffusion Model
Under real market conditions, there exist many cases when it is inevitable to adopt numerical approximations of option prices due to non-existence of...
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Modeling and Approximated Procedure Life Insurance Bond by the Stochastic Mortality and Short Interest Rate
Nowadays, the connection of the insurance industry to financial markets is very important because of unpredictable fortuitous events. A type of these...
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The Future of Probability
Probability as a subject in and of itself has rarely been truly appreciated by mathematicians in other disciplines. This has gradually changed over...
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Option Prices in Complete and Incomplete Markets
Already in the introductory Chap. 1 an introduction is given in a non-technical way to the basic...
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Numerical Method (2): Binomial and Trinomial Trees
As a lattice approach, tree methods, pioneered by Cox, Ross, and Rubinstein in 1979 (Cox et al., J. Financ. Econ. 7(3):229–263, 1979), employ a...
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Itô-Taylor Expansion Method of European Spread Option Pricing for Multivariate Diffusions with Jumps
In this paper, we propose a new method for spread option pricing under the multivariate irreducible diffusions without jumps and with different types...
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Error Analysis of Nonlinear Time Fractional Mobile/Immobile Advection-Diffusion Equation with Weakly Singular Solutions
In this paper, a weighted and shifted Grünwald-Letnikov difference (WSGD) Legendre spectral method is proposed to solve the two-dimensional nonlinear...
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Hedging with physical or cash settlement under transient multiplicative price impact
We solve the superhedging problem for European options in an illiquid extension of the Black–Scholes model, in which transactions have transient...
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A Deposit Insurance Pricing with a Multi-state Regime-Switching Volatility
Deposit insurance is a financial tool that guarantees the bank’s depositors from banks’ failure to maintain their assets. The dynamic of banks’...
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Numerical solution using radial basis functions for multidimensional fractional partial differential equations of type Black–Scholes
In this paper, as far as the authors know, for the first time, a one-dimensional partial differential model is generalized using fractional...
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Homotopy Analysis Method for Portfolio Optimization Problem Under the 3/2 Model
This paper considers the Merton portfolio optimization problem for an investor that aims at maximizing the expected power utility of the terminal...
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A Stable Time-Dependent Mesh Method for Generalized Credit Rating Migration Problem
The r-adaptive difference scheme is advanced in this article for solving the generalized credit rating migration model for arbitrary volatility with...
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Semi-implicit FEM for the valuation of American options under the Heston model
In this paper, we present an efficient numerical method for the valuation of American put options under the Heston model. Firstly, by adding a...
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Errors in the IMEX-BDF-OS methods for pricing American style options under the jump-diffusion model
The operator splitting method has been effectively applied to jump-diffusion models, and it is also easy to implement because the differential and...
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How Vulnerable Are Our Banking Systems?
The financial crisis that started in 2008 brought down several banks and led to a prolonged global recession. Many blamed the...
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Implicit-explicit Runge–Kutta methods for pricing financial derivatives in state-dependent regime-switching jump-diffusion models
In this paper, we have devised a novel class of implicit-explicit Runge–Kutta methods for the valuation of financial derivatives under...
