## Tagged Questions

1answer
266 views

### Mathematical properties of financial prices

Prices of financial assets (stock-market prices or currency exchange rates) obviously resemble trajectories of stochastic processes. What is known about their mathematical prope …
0answers
193 views

### American put option pricing by “binomial trees”

Dear MO World, I'm teaching a financial mathematics course and have found a fascinating (to me) numerical phenomenon and wonder if anyone has studied it, or knows anything similar …
1answer
221 views

### Trajectorial version of Doob’s $L^2$ inequality

In the paper http://www.mat.univie.ac.at/~schachermayer/pubs/preprnts/prpr0154.pdf you can find a trajectorial version of Doob's inequality. It is given by: \bar{s}^2_T+4\su …
10answers
2k views

### 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, …
1answer
220 views

### 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 lea …
2answers
526 views

### Compactness of the set of densities of equivalent martingale measures

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 …
10answers
886 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 dist …
2answers
149 views

### 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 der …
1answer
204 views

### 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 …
0answers
73 views

### 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 replicat …
5answers
2k views

### Discrete version of Ito’s lemma

Could anyone give me some references where I could find (a) discrete version(s) of Ito's lemma (b) a proof how it converges to the continuous form in the limit (c) its usage within …
3answers
4k views

### Visualisation of Riemann-Stieltjes-Integrals

The Riemann-Stieltjes-Integral $\int_a^bf(x)dg(x)$ is a generalization of the Riemann Integral. It is e.g. heavily used as a starting point for stochastic integration. The approxim …
3answers
1k views

### Rigorous definition, detection and test for trending vs. mean-reverting behaviour of stochastic processes

This is a question that has haunted me for some time. In the domain of time series you always talk about trends and mean reversion. But at least to me these concepts are either def …
1answer
347 views

### Better understanding of the Datar Mathews Method - Real Option Pricing [closed]

Hi all, in their paper "European Real Options: An intuitive algorithm for the Black and Scholes Formula" Datar and Mathews provide a proof in the appendix on page 50, which is not …
1answer
9k views

### Covariance and standard deviation relationship

I would like to know if an increase in the covariance between two variables would imply that the standard deviation for one of the variables has increased? This is assuming that t …

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