# Questions tagged [portfolio-theory]

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### 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 ...
60 views

### Mean Variance Optimization in a Utility Maximization Framework

I'm struggling to gain a broad understanding of Mean-Variance utility theory as it relates to finding the efficient frontier of a group of assets which each have some return and variance. The typical ...
161 views

### Fundamental Theorem of Asset Pricing (Linear Algebra)

I saw this question in a textbook that I was recently reading and don't really know how to aprpoach this problem. Let $H$ be a finite dimensional vector space with inner product ($\cdotp$, $\cdotp$)....
239 views

### Calculating the optimal portfolio for an investor with quadratic utility

The problem is from Asset Pricing and Portfolio Theory by Back and can be found here. The relevant info from section 2.5 can be found here. Given that we have the Expected value and the variance of ...
11 views

### Simple mortgage portfolio amortization

I have a large residential mortgage portfolio that has fixed and arm mortgages. I want to roughly calculate the amortization of the arm portfolio by year without delving into loan by loan calculations....
16 views

### Empirical estimates of beta for Mean-variance model

I need to evaluate a lottery according to mean-variance formulation for utility. That is to say, given a lottery X, its utility is given by U(X) = E(X) - bVar(X) where E(X) and Var(X) are the mean ...