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8

Feynman–Kac Theorem: Assume that $F$ is a solution to the boundary value problem \begin{align} &F_t+\mu(t,x)F_x+\frac{1}{2}\sigma^2(t,x)F_{xx}-rF=0\\ &F(T,x)=\Phi(x), \end{align} Assume furthermore that the process $e^{-r_s}\sigma(s,X_s)F_s$ is in $\mathcal L^2$ where \begin{align} dX_s=\mu(s,x)ds+\sigma(s,x)dW_s, \end{align} then $F$ has the ...


3

You can calculate Future Value with Matlab as follow FutureVal = fvdisc(Settle, Maturity, Price, Discount, Basis) Settle: Settlement date. Maturity: Exercise date. Price: present value of the security. Discount: Bank discount rate of the security. Basis: Day-count basis of the instrument(actual/360) For example, Settle = '03/15/2015'; Maturity = ...


1

The time $0$ forward rate from tme $n-1$ to time $n$ is \begin{equation} 1 + i_0(n-1, n) = \dfrac{(1 + s_0(n))^n}{(1+s_0(n-1))^{n-1}} \end{equation} where $s_0(n)$ is the $n$-year spot rate and $i_0(n-1, n)$ is the time $0$ forward rate from time $n-1$ to time $n$. The term structure of interest rates must be increasing to avoid arbitrage opportunities. ...


4

There are many books about revenue analytic and management: 1.Segmentation, Revenue Management and Pricing Analytic(2014). 2.Revenue Management(2011) 3.Revenue vs. needs : an analytical approach 4.Freemium Economics: Leveraging Analytics and User Segmentation to Drive Revenue(2013) 5.Marketing Analytics: Strategic Models and Metrics(2013)


6

Your questions is unclear but I guess you mean that for the return of stock A you find a model $$ r_A = (0.5, 0.75) (r_F^1, r_F^2) + \epsilon_A $$ where $r_F^i$ are the factor returns and $\epsilon_A $ is an uncorrelated error. Let us denote $e_A = (0.5, 0.75)$, the exposure of stock $A$ to the factors. For $B$ you have $$ r_B = (0.75, 0.5) (r_F^1, r_F^2) ...


2

The factors are the same for both stocks, so there is just one factor covariance matrix for both A and B. Factor models are a way to reduce the dimension of a problem. If every stock had its own set of factors, this would increase the problem dimension.


1

Your question is little broad and has two aspect: Theory and Application. If you are interested in scientific approach and academic literature this kind of thing is called Mathematical_optimization which is branch of Multi-objective optimization which is again a branch of Operations_research. In terms of mathematics of solving these problems multivariate ...


5

Yes, a Monte Carlo simulation (MC) is what you need. It is a well known and documented approach with many uses in finance, science and engineering. MC simulations are used to simulate the returns of complex financial assets or in your case returns of business ventures under uncertainty. Your input variables ($x_1, x_2,\cdots, x_n$) are uncertain. If you ...


0

I would try a Gradient Descent algorithm if possible, although this might take a little VBA knowledge. In general, finding the absolute minimum of a multidimensional problem like that is complicated and time consuming, but the gradient descent will find a local minimum easily. What you will need to do for worst case scenarios: Construct a cost function ...


0

My personal preference is to use OIS rate for recent years, and LIBOR when OIS isn't available. If neither is available, CB target rate can also be used.


1

Let Ri be the monthly returns (R1 for Jan, R2 for Feb, etc) Let Ci the the cumulative returns (C0= 0, C1=R1, C2=R1+R2, etc) Let AWCi be the above water cumulative return, defined as AWCi=MAX[0,Ci] In any month, the manager "receives" 0.2*[AWCi-AWC{i-1}] ; I say receives in quotes because this number can be negative. Then the investor receives the rest of ...


1

I believe in the literature they use either the T-bill rate or short term bank deposit rate.


0

Your answer is correct. The point is you need to match the interest rate periods with the compounding periods. So if (R/N) is the rate for a 1-month period, then "NT" must be the number of compounding months. Since you are compounding for 10.5 years, this represents 126 months (10.5 * 12). If, on the other hand, your compounding is semiannual (as is usual ...


0

If your compound period is monthly, then what you have is correct.



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