# Questions tagged [stochastic-calculus]

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### One-step Binomial model's Radon-Nikodym derivative

In the one-step binomial model... Question 1: What exactly is a '$\frac{d \mathbb Q}{d \mathbb P}$'? I think it's $\frac{d \mathbb Q}{d \mathbb P} = \frac{q_u}{p_u}1_u + \frac{q_d}{p_d}1_d$, so it's ...
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### Which Is The Better Way To Calculate Marginal Revenue? Using Derivative Or R(Q)-R(Q-1)?

I Still A Bit Confused About Marginal Revenue. Since Marginal Revenue Is The Additional Revenue We Get From Producing 1 Additional Good. That Means Marginal Revenue Is R(Q) - R(Q-1). My Teacher Says ...
88 views

### Do real life economists and financial analysts actually use calculus in their jobs?

From what I understand a lot of calculus is used at university level when studying economics and some finance courses (correct me if I'm wrong) but I was just wondering if economists and financial ...
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### Apply Ito's Lemma to exponential martingale

$\newcommand{\dd}{\, \mathrm{d}}$ Consider the exponential martingale, $$\xi_t^\lambda = \exp \left\{ - \int_0^t \lambda_s \dd z_s - \frac 12 \int_0^T \lambda_s^2 \dd s \right\},$$ that is used in ...
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### Intuition of the Kolmogorov Equations

So I understand the derivation of the Kolmogorov Forward and Backward Equations, but I don't quite understand the intuition. Here is from Stokey, 2008: "The backward equation involves time $t$ and ...
499 views

### How do I use the Malliavin calculus to solve for the optimal trading strategy in the classic Merton problem?

How do I use the Malliavin calculus to solve for the optimal trading strategy in the classic Merton problem? In Duffie's book "Dynamic Asset Pricing," he outlines the "Martingale method" of solving ...