# Questions tagged [mathematical-finance]

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

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### Relationship between an optimizer and a mode/mean of pdf

Let $X$ be a random variable, uniformly distributed over a support $S$. Let $f(X;\theta)$ be a function of $X$, parameterized by $\theta$. I am hoping to think of a relationship between two quantities:...
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### Solving an Ornstein-Uhlenbeck-like SDE $y(t,T)=H_t + \mathbb{E}[\int_t^T y(s-,T)dX_s|\mathcal{F}_t]$

I have asked a similar question involving some finance background some time ago here math.stackexchange, however no really good answer came up. I was able to find a solution at least for a special ...
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### market completion in stochastic volatility model

Hi all, Consider a stochastic volatility model. As there are two sources of risk and one asset only, this is an imcomplete market. One can complete the market by considering a derivative V1 used to ...
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### stochastic volatility valuation equation

I'm trying to derive the valuation equation under a general stochastic volatility model. What one can read in the litterature is the following reasonning: One consider a replicating self-financing ...
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### Arbitrage free price of a derivative when the price is collected over the lifetime of the derivative [closed]

Let $X_t$ be an american style financial derivative with random exercise time $T$ where $t$ and $T$ belongs to some finite set $A$. Buying this derivative requires the buyer to pay $p_t$ up to time $T$... 1k views

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### Expected value as decision criterion in the context of rare events

I have often seen discussions of what actions to take in the context of rare events in terms of expected value. For example, if a lottery has a 1 in 100 million chance of winning, and delivers a ...
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### Stieltjes integrals of predictable processes

I am looking for a direct proof of the fact that, roughly speaking, if $S=S_0+A+M$ is an $L^2$ semimartingale, and $M$ (the martingale part) has the martingale representation property, then for any ...
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Let $X_t\in\mathbb{R}$ be an Ito diffusion process given by $$dX_t=a(b-X_t)dt+\sigma dW_t$$, then the characteristic operator of $X_t$ is given by L=a(b-x)\frac{\partial}{\partial x}+\frac{\sigma^...