# Questions tagged [mathematical-finance]

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

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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

Consider an incomplete market $(\Omega,\mathcal F,\mathbb P)$ driven by a semimartingale $S=(S_t)_{t\in[0,T]}$. Under the no free lunch under vanishing risk (NFLVR) assumption, the set $\mathcal P^\... 10 votes 10 answers 1k views ### Is there any straightforward way to substitute for Gaussian/Brownian assumptions in financial mathematics? A huge amount of financial mathematics assumes Gaussian distributions of risks and Brownian movement of prices. What efforts have there been to replace these with heavy-tailed distributions? For ... 3 votes 0 answers 514 views ### Laplace transform of a stopping time for stochastic volatility models Let$V_t$be a solution of the SDE $$dV_t=V_t(rdt+\sigma_t dW_t)$$ where$\sigma_t$satisfies some other SDE $$d\sigma_t=\alpha(t,\sigma_t)dt+\beta(t,\sigma_t)dW^{\\ \prime}_t$$ and$W_t$and$...
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 ...