تحقیق در عملیات Operational Research with Risk

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شرح پروژه

توضیحات در فایل ورد ضمیمه شده است و میتوانید با دانلود افیل ضمیمه توضیحات را بهتر ببینید.

code ➕1500 words report  4days

Subject：专业是什么

Operational Research with Risk

Project/Topic：  要做一个什么项目

Dynamic scenario selection for stochastic programming

Report/words count: 要写多少字

Aim of project: 要研究什么课题

The second assignment for "Optimization Methods in Finance" was using the following setup: You seek to divide your money into 8 different investment opportunities in order to maxmimise expected return (actually minimize expected shortfall relative to a return target). Future return of the investments are unknown but are assumed to be described (exactly) by 100000 (equally likely) future scenarios. Your aim is to find the investment that minimizes expected shortfall subject to these 100000 scenarios.

Unfortunately solving this problem is very expensive, so you seek a cheaper way of solving the problem approximately. In OMF assignment 2 various avenues were explored, for example only using 10 well chosen scenarios as an approximation (these can be found by clustering) or using stochastic gradient methods.

The aim of this project is to follow up with more sophisticated approaches:

- After solving the problem with 10 scenarios one could try to identify which other scenarios should be added (or how the 10 scenarios should be modifed) in order to improve the performance of the investment.

- One could try to estimate the difference between the predicted performance of the investment (evaluated over the 10 chosen scenarios) and the real performance (measure by evaluating expected shortfall over all 100000 scenarios) - i.e. the model error and use this estimate as a correction to the 10-scenario model.

Tool: 要用什么工具，例如Python。Java matlab

 Matlab cvx tool

What else: 你有什么要嘱咐的

My understand of project:

Using assignment’s set up: invest budget of B =£10, 000 into the 8 assets, L =£10,100, my aim is to find the investment that minimizes expected shortfall subject to these 100000 scenarios.  Should I just use retm.mat(quesiton1 of assignment 2) from Learn for returns?

Do I need to use stochastic gradient methods to solve the problem with 10 scenarios first, then apply papers’ ideas?

There are three ideas according to papers: 1). Identify critical region for risk measure.2）learn over several iterations where to place the scenarios. 3).Use importance sampling .So I need construct new models according these ideas then select 100 scenarios and analysis investment decisions (report in-sample and out-of-sample expected shortfall).------all three ideas should be applied

The implement must follow papers’ ideas and assignment’s requirements.

I need some explanations to understand every codes’ function and request for mathematical formulations and result analysis (1.tables and figures should be presented like assignment and papers 2.applied algorithm for projects 3.data discussion )

The explanations for files

Papers:

a) Fairbrother/Turner/Wallace + Garcia-Betrand/Minguez are about CVaR 

optimization by trying to identify the region that is contributing to 

CVaR/expected shortfall and placing scenarios there.  Garcia/Minguez 

describe a way in which you try to learn over several iterations where 

to place the scenarios.

b) The Papavisilou/Oren paper is a more general applicable approach to 

focus on the "important scenarios": the idea is to solve a problem with 

a given scenario set, then use the solution to find a new weighting of 

all 100000 scenarios and sample from the 100000 scenarios with the new 

weighting to find a new selection of 10 scenarios.Note that this paper 

is in the context of an Energy Optimization application, but the 

framework can be used anywhere. So ignore the sections on energy and 

just look at Section 6.The algorithm is:

- choose a small number of scenarios N (N=10, or N=100 in our case) as before. Solve the problem to find an optimal investment policy x.

- choose a much larger number of scenarios M (could be M=100,000 so all of them)

- evaluate the expected shortfall (C(w) for all scenarios in this large set under the policy x obtained above)

- calculate q(w) for each scenario in M according to (53)

- sample N scenarios out of M with sampling probability q(w).

Assignments：

There are origin requirements and data。

Also there are some answers and the version of my work

مهارت ها و تخصص های مورد نیاز

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