# Questions tagged [stochastic-control]

Stochastic control is widely used in finance since it is about decision taking in a random environment. Option replication, portfolio construction, intraday trading are typical applications of stochastic control.

43 questions
Filter by
Sorted by
Tagged with
136 views

### A quant job interview question about (toy) futures

On Monday, you receive prices for each day of the week: $X_{1,1}, \ldots, X_{1,5}$. On Tuesday, you receive prices for Tuesday, Wednesday, Thursday, and Friday: $X_{2,2}, \ldots, X_{2,5}$. On ...
• 151
49 views

### Asset pricing based on stochastic inflation discounting (inflation controlled by stochastic state variable)

Suppose there is an asset that pays fixed nominal payout $\delta_t = \delta$, with a constant real discount rate $\bar{r}$ and stochastic inflation $\pi_t$. Suppose the price follows a controlled ...
212 views

### Understanding the calibration of High-frequency trading in a limit order book

I am trying understand and replicate this thesis, which is based on, High-frequency trading in a limit order book by (Avellaneda and Stoikov, 2008) and Optimal market making, by Olivier Gueant, 2017, ...
1 vote
311 views

### Is stochastic control with the HJB equation used in market making/algo trading at institutions?

In chapter 5 of https://www.maths.ed.ac.uk/~dsiska/LecNotesSCDAA.pdf, they use stochastic control and the Hamiltonian Jacobi Bellman (HJB) equation in attempt to measure bid-ask spreads and optimal ...
90 views

### Beta Weighting Deltas: What happens to the non-correlation part?

At various informational websites about option trading, it is often mentioned that in order to compare different underlyings in an apples-to-apples comparison, it is useful to beta-weight the deltas. ...
202 views

### American option pricing formulation

Assuming the usual setup of: $\left(\Omega, \mathcal{S}, \mathbb{P}\right)$ our probability space endowed with a filtration $\mathbb{F}=\left(\mathcal{F}_t\right)_{t\in[0,T]}$, $T>0$ denoting the ...
• 51
276 views

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

Suppose that $(\Omega,\mathcal{F},\mathbb{P})$ is a standard probability space and $Z_t=(Z_t^1,Z_t^2)$ is a two dimensional Brownian motion with the filtration $\mathcal{F}^Z_{t}$ and $Z_t^1$, $Z_t^2$ ...
• 141
1 vote
99 views

### How to derive this HJB equation?

I'm reading the paper by J.Gatheral and A.Schied (2012) - "Optimal Trade Execution under Geometric Brownian Motion in the Almgren and Chriss Framework". On page 6, the authors provide a ...
1 vote
63 views

### optimal log growth under a path dependent GBM

Consider an extension to the (one-dimensional) geometric Brownian motion model, $$dS_t = \mu(t,S_.)S_t dt + \sigma(t, S_.)S_t dB_t,$$ where $\mu$ and $\sigma$ are previsible path functionals, i.e. ...
• 247
160 views

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

Basic question: Can we generalize the HJB PDE to apply to optimal controls of non-Markovian/path-dependent SDEs? Specifically, how do we generalize the log-optimal portfolio to path-dependent ...
• 247
558 views

### References for Stochastic Control for finance

What are some good references to study Stochastic Control with applications to Finance, like the Merton problem and other variants? Books or review papers?
371 views

### Solving option market making problem

I am currently working on a paper for quoting option as a market maker from Bastien Baldacci , Philippe Bergault & Olivier Guéant Without dwelling on details on how to obtain the HJB equation for ...
• 98
660 views

### Game theory and stochastic calculus

Does anybody know any details of game theory literature combined with stochastic calculus in finance? If yes, please recommend some papers of any authors who are doing exceptional work on the filed. ...
• 193
189 views

• 711
78 views

• 711
1 vote
204 views

### Closed-form solution to optimal single assset position sizing with predicted returns

Say that I observe a predictor $w_t \sim N(0,\sigma_1)$ for the returns in a single asset over the next time interval: $$r_t = \alpha w_{t-1} + z_t$$ where $z_t \sim N(0,\sigma_2)$ is unobserved ...
• 537
111 views

### Portfolio insurance strategy with path dependence

I have the following problem. Let us assume that $S_t$, the stock price follows, geometric Brownian moation with parameters $(\mu,\sigma^2)$. We are given an amount of money $M$ and at each point in ...
• 13.7k
427 views

### Lipschitz condition in mathematical finance

I am interested in a rigorous explanation on why the Lipschitz condition plays a major part in stochastic calculus, most significantly in mathematical finance. To be specific, suppose we want to ...
• 483
1 vote
31 views

### Is there any theoretical work to find an optimum size for the size of horizon in finite-horizon optimization or control?

we learn a lot about finite and infinite horizon control in dynamic programming. but I was wondering if we want to minimize the cost per time(discrete time) is there any work to find the optimum size ...
• 111