A Note on Almgren–Chriss Optimal Execution Problem with Geometric Brownian Motion
نویسندگان
چکیده
We solve explicitly the Almgren–Chriss optimal liquidation problem where stock price process follows a geometric Brownian motion. Our technique is to work in terms of cash and use functional analysis tools. show that this framework extends readily case stochastic drift for portfolio.
منابع مشابه
A Note on Gravitational Brownian Motion
ABSTRACT Chandrasekhar’s theory of stellar encounters predicts a dependence of the Brownian motion of a massive particle on the velocity distribution of the perturbing stars. One consequence is that the expectation value of the massive object’s kinetic energy can be different from that of the perturbers. This effect is shown to be modest however, and substantially smaller than claimed in a rece...
متن کاملExact solutions for Fokker-Plank equation of geometric Brownian motion with Lie point symmetries
In this paper Lie symmetry analysis is applied to find new solution for Fokker Plank equation of geometric Brownian motion. This analysis classifies the solution format of the Fokker Plank equation.
متن کامل1 Geometric Brownian motion
where X(t) = σB(t) + μt is BM with drift and S(0) = S0 > 0 is the intial value. We view S(t) as the price per share at time t of a risky asset such as stock. Taking logarithms yields back the BM; X(t) = ln(S(t)/S0) = ln(S(t))− ln(S0). ln(S(t)) = ln(S0) +X(t) is normal with mean μt + ln(S0), and variance σ2t; thus, for each t, S(t) has a lognormal distribution. As we will see in Section 1.4: let...
متن کاملOptimal Executive Compensation when Firm Size Follows Geometric Brownian Motion
This paper studies a continuous-time agency model in which the agent controls the drift of the geometric Brownian motion firm size. The changing firm size generates partial incentives, analogous to awarding the agent equity shares according to her continuation payoff. When the agent is as patient as investors, performance-based stock grants implement the optimal contract. Our model generates a ...
متن کاملSimulating Brownian motion ( BM ) and geometric Brownian
2) and 3) together can be summarized by: If t0 = 0 < t1 < t2 < · · · < tk, then the increment rvs B(ti) − B(ti−1), i ∈ {1, . . . k}, are independent with B(ti) − B(ti−1) ∼ N(0, ti − ti−1) (normal with mean 0 and variance ti − ti−1). In particular, B(ti) − B(ti−1) is independent of B(ti−1) = B(ti−1)−B(0). If we only wish to simulate B(t) at one fixed value t, then we need only generate a unit no...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Market microstructure and liquidity
سال: 2021
ISSN: ['2424-8037', '2382-6266']
DOI: https://doi.org/10.1142/s2382626620500057