Questions tagged [finance]
Questions related to the various aspects of financial mathematics. Topics include option pricing, arbitrage theory, market completeness and stochastic analysis.
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Is there a notion of approximation of continuous-time Markov processes by finite-valued Markov processes?
Recall that in practice, to simulate a Brownian motion on $[0,1]$, we usually use the interpolated process $X^n=(X^n_t)_{t\in[0,1]}$ between the jumps of a random walk $(S_k)_{k=1,...,n}$ with $n$-...
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How to calculate loan face value of "dicount instalment loan" [closed]
I am trying to calculate face value (face_value) of "discount instalment loan" and monthly_repayments. In this type of loan bank would calculate interest of the loan over given period ...
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How to solve for monthly interest rate given principal, number of payments, and total payment
The problem:
A lottery winner is given two payment options: Receive 131 million dollars in 25 yearly installments of equal size, the first payable immediately, or receive a single immediate payment of ...
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Two-stage stochastic process with recurse
I'm trying to learn how to optimize a portfolio using Markowitz MVO with a two-stage stochastic process with recurse.
What I did is:
got assets' prices;
tuned them into log;
got the log returns;
Used ...
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Analytical function from summation representing Dollar Cost Averaging
I would like to understand what is the math necessary to go from a summation representing the Dollar Cost Averaging (DCA) to the analytical function.
In DCA, a certain capital $C_0$ is invested ...
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No Arbitrage iff no generalized Arbitrage
Let’s consider a market in finite discrete time with trading dates $0,1,\dots,T$ probability space $(\Omega, \mathcal{F}, \mathbb{P})$, filtration $\{\mathcal{F_t}\}_{t \in \{0,1, \dots, T\}}$, $N$ ...
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Should I consider the price for "option pricing" problem?
I'm trying to solve the following problem from "Probability and Statistics" book by Morris H. DeGroot and Mark J. Schervish.
Suppose that common stock in the up-and-coming company A is ...
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How to formally justify fudge factor in this difference equation solution?
In Exercise $11$ from Section $3.3$ of Differential Equations With Boundary Value Problems by Polking, Boggess, and Arnold, we first develop the difference equation $P[n + 1] = (1 + \frac{I}{m})P[n],\ ...
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What formula would I use to calculate total income over $x$ years with a fixed salary increase rate.
I'm wanting to calculate how much total money I would have earned over x amount of years, but while accounting for increase in pay at the end of each year (or maybe even continuous?)
Lets say for ...
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Financial based equation for Cash Flow analysis on Annuity ( Sequences and Series Analysis)
I have a particular Annuity type of question.
I am familiar with all the Cash Flow type of equations such as Present Value, Future Value for compound interest, and for Annuities and Mortgages etc.
...
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For $A_t= B_t^l Y_t \mathbb{E}(\frac{A_T}{B_T^l Y_T} \mid \mathcal{F}_t)$, find the values of $l$ to replicate $A_t$ by a self financing portfolio $X$
Background:
In attempting to resolve the below problem, I have arrived at an answer that appears to counter intuition (and therefore, I suspect that it is wrong). I would appreciate assistance in ...
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Why does total salary differ over 5 years if the average salary increase averages to the same?
I'm considering 2 general scenarios of both having an average salary increase of 6% over 5 years. But in the first scenario, the person ends up with a lower total salary compared to the second ...
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Analyzing Expected Profit in a Symmetric Random Walk with Trading Actions
Problem Formalization:
I am examining a problem where a stock price $X_t$ follows a symmetric random walk starting at 10, and increments or decrements by 1 unit at each step with equal likelihood. The ...
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Proof that annual nominal interest rate, convertible $m$ times in a year, is a decreasing function
I'm reading the following notes on financial mathematics (they are in italian).
In here the annual nominal interest rate, convertible $m$ times in a year, is defined as (page 32)
$$j(m)=m i_{1/m}$$
it ...
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Question regarding a value in a one-period model
There is a script at my university (can't post it for copyright reasons) for a course on discrete time financial mathematics. I decided to give it a try and found this problem:
Consider a financial ...
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