# Tag Info

### References for Stochastic Control for finance

Peter Forsyth of UWaterloo is my favourite author on this topic (one of my top three in MathFin!) Personal Homepage with Lots of Papers Optimal allocation under wealth goals, optimal decumulation ...

### Code examples of solving Stochastic Optimal Control problems

FWIW, I implemented one such control solution for my course project. See here
Accepted

### example Hamilton-Jacobi-Bellman Equation - clarification of $dX_t$ derivation using $\pi_t$, $\Pi_t$

We assume that \begin{align*} \frac{dX_t}{X_t} &= (r+\pi Y_t)dt + \pi\sigma dW_t,\tag{1}\\ dY_t &= -\lambda Y_t + dB_t.\tag{2} \end{align*} From $(2)$, \begin{align*} Y_t = Y_0 e^{-\lambda t}...
Accepted

### Question on derivation step in portfolio replication under different borrowing and lending rates

Noting that $$B= V -\alpha S = V - (\alpha S)^+ + (\alpha S)^-$$ $$= (V - (\alpha S)^+)^+ - (V - (\alpha S)^+)^- + (\alpha S)^-,$$ a clearer way to write the dynamics of the funding costs (funding ...

### How do your solve for trader's optimal demand in market similar to Kyle's model?

Generic knowledge about this kind of models Let me try to get your model close to elements that are known: Time continuous Kyle's model is something that is solved in Çetin, Umut, and Albina Danilova....

### References for Stochastic Control for finance

Look into Huyên Pham, Continuous-time Stochastic Control and Optimization with Financial Applications; Salvatore Federico, Giorgio Ferrari, Luca Regis (Editors). Applications of Stochastic Optimal ...

### How to, from various hypotheses on the P&L, get known models (BS, Heston etc ...)

You can characterize local volatility (LV) models by the existence of a delta-hedging strategy which reduces the variance of P&L to zero, together with an assumption that P&L is a continuous ...
Accepted

### Merton portfolio allocation problem proportions/weights >1 or <0?

Your statement should be correct, the weights into the risky asset are not bounded between $0$ and $1$. Essentially, by setting $r=0$ you omit the term which shows that your weights always sum up to ...

1 vote

### non-Markovian/path-dependent optimal log utility and HJB-PDE

This answer will provide somewhat of an educated guess, but is by no means rigorous or exact. It is based on my preliminary readings/understanding of subsections 5.4.1 and 5.4.2 of Applied Stochastic ...
1 vote

### The duality of the free energy and relative entropy used to deduce deduce the stochastic game between an agent and the market

Such relationships are commonly covered in statistical mechanics, so any decent statsictal mechanics book should help. Here is an article that gives a very nice summary of the key concepts: https://...
1 vote

1 vote

### Stochastic optimization and mean field games : textbooks

I answer my own question. A starting point would be : the summer school on mean field games, provided by the University of Chicago. summer school
1 vote

### Understanding the HJM drift condition's dimensions

Your issue is that you misinterpreted the NA criterion, it reads: $$a_t(x) \triangleq \sum_{i=1}^{\infty} \left(b^i_t(x) \int_0^x (b_t^i(u))^T du\right)e_i,$$ where $b^i_t$ denotes the $i^{th}$ ...
1 vote
Accepted

### optimal strategy problem (using Jensen's inequality)

I assume that the problem is $$\max_{\pi} E\left(\ln Z_T^{\Pi} \right).$$ Note that $\ln Z_t^{\Pi} = \ln X_t^{\Pi} -\ln X_t^{\rho}$. Moreover, \begin{align*} d\ln Z_t^{\Pi} &= d\ln X_t^{\Pi} -d\ln ...
1 vote
Accepted

### trading strategy problem - initial capital x buys S over time [0,T] at the constant rate of x/T euros per unit of time

Equations (1) to (3) are correct. Your investment strategy is then, $\forall t > 0$ $$X_t = \theta _ t S_t$$ Provided you use this strategy as part of self-financing portfolio you can write the P&...
1 vote
Accepted

### investor terminal value of portfolio with two risky assets 1) correlated 2)not correlated $\phi_t^1=S^{2}_{t}, \ \phi_t^2=S^{1}_{t}$

Let $Y_t := 2 S_t^1 S_t^2$. Applying (multivariate) Itô to the function $f(t,S_t^1,S_t^2)=2 S_t^1 S_t^2$ yields a stochastic differential equation for $Y_t$  \frac{dY_t}{Y_t} = \frac{dS_t^1}{S_t^1}...

Only top scored, non community-wiki answers of a minimum length are eligible