# 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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### Question related to profit/loss.

Guys see this question: For what sum should goods worth Rs. 1150 be insured at 8% so that in case of loss the owner may recover the premium as well as the goods? I can't understand the meaning ...
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### Is this equation a parabola or a hyperbola?

In a 1972 paper by Robert Merton, the following equation is derived: $$\sigma(\mu;A,B,C,D)=\sqrt{\frac{A \mu^2-2B\mu+C}{D}}$$ This is known as the Markowitz frontier in finance. When this is ...
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### Looking for a “Black-Scholes-esque” expression for $E[\max(V-K,Y)]$

In Hull (2008, p. 307), the following equation is found (Eq. 13A.2): $$E[\max(V-K,0)]=\int_{K}^{\infty} (V-K)g(V)\:dV$$ Where $g(V)$ is the PDF of $V$, $K$ is a constant, and both $V,K>0$. He ...
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### Financial Mathematics, Simple interest question. Help.

Laurie deposits $\$60,000$in a bank at$5\%$interest per annum. Andrew deposits$\$40,000$ in bank at $8\%$ per annum. How long wil it take, by simple interest, for Andrew to have more money ...
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### Improper integral confusing step

The following passage is in my textbook: $$A(S) = \int_0^{\infty} f(E) \max(S-E,0)dE$$ This simplifies to $$A(S) = \int_0^{S} f(E)(S-E) dE$$ Now this is from a finance textbook so it might ...
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### Lemme itô and Martingale [closed]

I want to to find values of $a$, $b$ such that the process: $$e^{W_{t}^2+at+b\int_\limits{0}^{t}W_{s}^2\,ds}$$ be a martingale Could you please help me do that Thank you
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### Estimating compound growth

I have a compound interest function with the following parameters: Value at time 0 = 13.8 Interest rate = 0.05 time interval = 10 I need to check quickly, (without a calculator, only pen and paper) ...
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### I'm trying to reverse engineer a formula to find answers without trial and error.

As an example, I need to pay €100 to this business, and there are 2 separate fees I need to also pay, the fee for the payment processor and the VAT (Value Added Tax). I know that the fee for the ...
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### Risk-neutral (i.e. martingale) measure if density is given for a single random variable (i.e. asset)

Let $(\Omega,\mathcal F, P)$ be a probability space. And let $S : \Omega \to \mathbb R$ be a random variable, called an asset, also we are given $\pi > 0$ called a price and some $r \ge 0$ called ...
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### Maximum value for a dependent variable in a marginal effect model

I am unsure as to whether my calculations are correct. Currently, the model given is: The first question was to derive an equation for the marginal effects of EDU on In(Wage). I obtained the ...
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### Ratio vs Difference in terms of growth

Suppose we have the following data: start date end date quantity 01/05/2014 07/05/2015 5 07/06/2015 02/06/2016 8 What ...
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### Automatic differentiation for finance

we're estimating sensitivities with automatic differentiation. What we have read about it the adjoint (reverse) should perform more efficiently than the forward mode when there are more input ...
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### No arbitrage iff there EMM $P^*$ theorem [closed]

The definition of an arbitrage I was given: "An arbitrage strategy is an admissible strategy with zero initial value and positive probability of a positive final value." I think that an initial ...
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### Interpretation of the Snell Envelope wrt European and American options.

In lectures we were taught that the Snell envelope U of a process Z, passes from European to American option prices. I thought that price processes are supposed to be martingales, but the Snell ...
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Brenda owes Cathy $\$8500$and has signed a promissory note to repay the debt in 15 months from the signing date. The note was signed on December 6, 2009, and the maturity value of the note is ... 1answer 83 views ### Ornstein–Uhlenbeck SDE. I am trying to understand the solution to the following exercise, however it is kind of poorly written. Can someone please explain it to me? For$V = (V_t)$the solution to the Ornstein-Uhlenbeck SDE ... 2answers 58 views ### Brownian motion and covariance Show that for$B = (B_t)$Brownian motion, its covariance is$cov(B_s, B_t) = min(s, t)$. The solution I was given was: For$s ≤ t$,$B_t = B_s + (B_t − B_s)$,$B_sB_t = B_s^2 + Bs(Bt − Bs)$... 0answers 37 views ### Common term for “present value” and “future value” In the past, I have always used the term "present value" for the value of a payment made at some point in time$t$from the perspective of some other valuation point in time$T$. I did not distinguish ... 1answer 82 views ### Martingale Properties Here is a proof of a property of a martingale$X$relative to the filtration$(F_{n})$:$n\gt m,\\\\ \\ E[X_n|F_m]=E[E[X_n|F_{n-1}]|F_m]=E[X_{n-1}|F_m]=...=E[X_m|F_m]=X_m$In the definition of a ... 1answer 274 views ### Redington vs full immunization? I understand that the present values and duration of liabilities and assets are required to be equal to each other under both cases, and furthermore for Redington immunization the convexity must also ... 1answer 19 views ### Ito's formula for this stochastic differential - please explain this step? Referring to those two lines, can someone please explain how those results were obtained? My understanding is, the following formula is being referenced: $$dV_t = dV(S_t,t) = \frac{\partial ... 0answers 49 views ### Is this a self-financing portfolio? I have S_t = 10 + B_t, \beta_t = 1, a_t = 2B_t, b_t = -t - B_t^2 - 20B_t Then the value, V = a_t S_t + b_t \beta_t Is this a self financing portfolio? Note, B_t is brownian motion I am ... 1answer 85 views ### Compounded Interest with Exponentially Increasing Periodic Payments Given the formula$$v_a = p\left(\frac{\left(1+\frac{r}{n}\right) ^{nt}-1}{\frac{r}{n}}\right)$$for the value$v_a$of an account growing at a periodic rate$r$with a regular deposit$p$compounded ... 1answer 83 views ### Single factor model question, related to the benefits of diversifying one's portfolio. The question: Suppose in a single period investment problem we may divide our wealth between n assets and that the return on the ith security is given by$r_i = \alpha + \beta_i\theta + \epsilon_i,$... 0answers 36 views ### Request for recommendation: Transition textbook for graduate course in mathematical finance or classical math reference book I am looking for a well-written, theoretically rigorous textbook that contains all the mathematics necessary to transition smoothly to a graduate course in mathematical finance. I am graduating with ... 1answer 42 views ### Prove$\sum \frac{t}{(1+y)^t }= \frac{y+1}{y^2}$I see on Wolfram Alpha that$\sum \frac{t}{(1+y)^t} = \frac{y+1}{y^2}$when t goes to infinity. I cannot, however, proove it myself. What theory is used and how do I start the proof? 1answer 117 views ### Regarding “Two Singular Diffusion Problems” by William Feller I'm currently reading the research paper, Two Singular Diffusion Problems, by William Feller (1950). However, I don't understand how Feller derived the solution$(3.5)$given equation$(3.4)$in his ... 0answers 48 views ### How to use the BA II Plus financial calculator to solve for IRR and NPV? I've calculated the answers manually but would like to learn how to do so on the financial calculator to save time on the test and minimize errors. How to do this? Problem: You have been offered a ... 2answers 46 views ### To mark up in retail by$20$%, do I add$0.20$times the original cost, or divide by$0.80$? Why is it that when I take a cost of say$\$15.60$ and want to mark the item up at retail 20% that I'm being told two different ways with two different answers? The first way (my way) would be to ...
Find a recurrence relation for the amount of money outstanding on a \$40,000 mortgage after n years. The interest rate on the mortgage is 10% and the yearly payment is \$2,000( the yearly payment is ...
Suppose that the APR on a certain product $x$ whose dollar value is $x_1$ is 5%. Now suppose we subtract some amount $x_2$ from $x_1$ where $x_2 < x_1$. Call this new amount $y$. How does one ...