# Tagged Questions

Questions having to do with financial mathematics. Please note that for questions in quantitative finance, quant.stackexchange.com is perhaps a better site.

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### In stochastic calculus, why do we have $(dt)^2=0$ and other results?

I'm doing actuarial problems of Exam MFE and it covers some of the stochastic calculus (like Ito's Lemma). One of the frequently used results are the so-called "multiplication rules": $(dt)^2=0$ ...
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### Mean-variance portfolio probelm

So the question asks: Consider three uncorrelated stocks in the market. Each stock has variance 1. The expected returns are given by $2, 3$ and $5$ respectively. Find the optimal mean-variance ...
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### Proof that no futures trading system always wins

Hopefully someone here has some knowledge in both finance and maths. I am pondering on the existence/impossibility of a trading system (or algorithm) that ALWAYS ends up winning money, no matter how ...
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### Stochastic control, numerical, need expectations given coupled SDEs

I'm looking at a trio of processes which arises in a stochastic control situation. I have a process $(V_t)$ which I may control, and $(V_t)$ influences a diffusive stock price process $(S_t)$. The ...
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### Analogue of Leibniz Rule for Stochastic Integrals

Suppose $$f(t,u)=f(0,u)+\int_0^t{\mu (w,u)dw}+\int_0^t{\sigma(w,u)dB_w}$$, where $B_w$ is a standard Brownian motion. I would like to calculus the drift and diffusion of $Y_t=-\int_t^s{f(t,u)du}$ (...
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### Standard practice for identifying outlying spend amounts

Hope this is mathematical enough to qualify as a question - I'm no mathematician! I have a set of individuals travel & entertainment credit card spend, and I'd like to highlight any outliers that ...
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### Brownian Bridge Probability

Doing a project I have found in some papers that the (discretised) probability of the Brownian Bridge (which has $S(n)$ as initial value and $S(n+1)$ as final value, where S follows a Geometric ...
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### Why is a risk neutral measure unique in a discrete time market with continuous states?

Why is the radon nikodym derivative unique in a discrete time market with continuous states? By radon nikodym derivative, I meant the derivative with respective to the risk neutral measure and the ...
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### Conditional expectation and set times random variable??

On page 62, what in the world is the meaning of equation (5.2)? $\mathcal{F}_t$ is a $\sigma$-algebra, so $Z_t \in \mathcal{F}_t$ is a set. $X_u$ is a random variable, so what is $Z_t X_u$?
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### implied volatility

I have a question about calculating the implied vol. Assuming the implied vol that a option will expire in 1 day is $\sigma_1$, and the implied vol that the option will expire in 2 days is $\sigma_2$. ...
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### subaddivity of VaR

It is known that the VaR (Value at risk) doesn't fulfill subadditivity, i.e. $VaR(X)+VaR(Y) \le VaR(X+Y)$. But for elliptical distributions subadditivity is true. Questions: (1) Which ...
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### Options on Futures Black-Sholes

I am taking the Financial Risk Management course, and the topic now is "Variations on the Black-Scholes Model". I am following Paul Wilmott's "The Mathematics of Financial Derivatives: A Student ...
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### Proof of the finiteness of integral (in option pricing)

I would like to ask for help with proving the finiteness of the following double integral. $$\int_{0}^{\infty}e^{\alpha+k}\int_{k+\zeta}^{\infty} (e^{-\zeta+x}-e^k)f(x)\ \mbox{d}x\ \mbox{d}k,$$ ...
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### Finance Algeabra: Converting a Discount Polynomial Function to an Interest Rate Polynomial Function

I have a finance problem that is 99% mathematical. In finance, the price of a bond could be modelled as the discounted value of its future cash flows, so something like: ...
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### Financial Mathematics--Finding Compounding Period given Annual and Effective Interest Rates

I'm trying to find a compounding period C when given an annual interest rate r and effective annual yield i. I'm working with the following equation: $i=(1+r/C)^C-1$ I'm having trouble re-writing ...
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### Calculating benefit of paying off loan ahead of time

So I'm doing a little financial planning, and I'm looking into the worthwhile-ness of paying off my student loans as quickly as possible. Being that I have multiple student loans, I combined them all ...
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### Relations between Call and Put

I am trying to solve a question in finance but I am pretty much stuck and would need your help :) Suppose you know the following information about a market: Future is at 66 70 strike straddle is ...
I have the following figures: (x) Quote for new software feature: $10,000 (y) Employee Rate:$15.00/hour (z) Hours per Day to perform task manually: 2 (n) Number of working days in a year: 251 (a)...