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# Optimal Portfolio Liquidation with a Markov Chain Approach

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## Jingnan Chen

on 8 October 2013

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#### Transcript of Optimal Portfolio Liquidation with a Markov Chain Approach

Optimal Portfolio Liquidation with a Markov Chain Approach
LiteRature ReView
ProBlem ForMulation
Objective
Ph.D. Candidate
University of Illinois at Urbana-Champaign

How to liquidate large blocks of assets in a short time period?
Price Impact
Market Volatility
VS
Limited Market Liquidity
PortFolio LiquiDation is CompliCated
R.Almgren and N.Chriss.
"Optimal Execution of Portfolio Transactions"

Price Dynamics:
Unaffected Price:
Executed Price:
Holding Dynamics:
QV:
VaR:
ContriButions
Propose efficient numerical method:
Markov chain approximation

Obtain analytical properties：
effect of price impact, risk-averse parameters and risk measures
Numerical Method
Bellman Equation:
Convergence Rate:
clear-cut O(1/n)!
Properties
Proposition:
With zero drift rate, the optimal initial selling rate is
decreasing
w.r.t.
price impact
, but
increasing
w.r.t.
risk aversion parameter.
Effect of Price Impact
Effect of Risk Aversion
Conclusion
Highly efficient DP algorithm
Analytical properties of optimal strategy
Thank You!
Jingnan Chen
Binomial Approach:
Multiple assets: BEG multi-variate binomial model
Single asset: CRR binomial model
MCA: build locally consistent discret Markov chain to approximate original continuous process
Question?
Numerical Example
Risk Measure: VaR
Optimal Solution=-75 share/sec
Our Work
1.
Asset price dynamics:
general geometric Brownian motion
3.
Comparison of risk measures:
2.
New numerical scheme:
Markov chain approximation
4.
Analytical properties：
effects of influential factors
Proposition:
When
is the risk measure, the optimal trading strategy is a pure
selling
program under zero drift rate.
Simulation Result
Price Dynamics: GBM
1. Mannual order
2. Automated execution algorithm
1. Simulate asset dynamics