# Questions tagged [mathematical-finance]

For questions about mathematical problems arising from the study of financial markets.

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### existence and uniqueness of solution to CEV model sde

Suppose that you have the CEV model for a stock price following the sde $$dS_t = r S_t dt + \sigma S_t^{\eta} dw_t$$ where $0 \leq \eta\leq 1$, $S_0=s_0$ and $w$ is a Brownian motion. How do you ...
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### Why are financial markets modeled by càdlàg processes?

When opening a book or reading an article on mathematical finance, financial markets (e.g. stock prices) are always modeled by càdlàg semimartingales. I was wondering why it is that these processes ...
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### Stochastic integral with respect to a random field

I came across a generalized Black-Scholes equation formulation in this paper. Let me highlight the basic idea below. Consider a random field $W(t,T)$ where for a fixed $T$, $W$ is a Brownian motion ...
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### Unique EMM & completeness in the Black-Scholes model

Consider the Black-Scholes model $$dS(t) = \mu(t) S(t) dt + \sigma(t) S(t) dW^{\mathbb{P}}(t)$$ $$dB(t) = r(t) B(t) dt$$ Steele shows now in "Stochastic Calculus & Financial Applications" (Ch. ...
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### Inverting the cumulative probability function to find roots of stochastic function

Given a function: $$f[x]=a\, \Phi \left[-x+\sigma \sqrt{\tau}\right]-\left(b+c\, e^{-d \tau}\right)\Phi \left[-x\right]$$ where $\Phi$ is the cumulative density function of the standard normal ...
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