# Questions tagged [mathematical-finance]

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### Tradeoff debt/equity Financial Problem [closed]

I am an MBA student and I'm having a hard time solving this issue, can someone please try and advise? that would be really really helpful! Consider a firm that has 5M dollars in cash, and a face-value ...
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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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### Construction of equivalent local martingale measures

Assuming No Free Lunch with Vanishing Risk (NFLVR), the market $(\Omega, \mathcal F, \mathbb P, S)$ admits a measure $\mathbb Q$ equivalent to $\mathbb P$ such that $S$ is a $\mathbb Q$-local ...
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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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