Asset liability management models in insurance and benchmark decomposition
This presentation is the property of its rightful owner.
Sponsored Links
1 / 24

Asset/Liability Management Models in Insurance and Benchmark Decomposition PowerPoint PPT Presentation


  • 59 Views
  • Uploaded on
  • Presentation posted in: General

Asset/Liability Management Models in Insurance and Benchmark Decomposition. Alexei A. Gaivoronski and Sergiy Krylov Norwegian University of Science and Technology. Contents. 1. Introduction: ALM model outline 2. Approximations: scenario trees parametric strategies

Download Presentation

Asset/Liability Management Models in Insurance and Benchmark Decomposition

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Asset liability management models in insurance and benchmark decomposition

Asset/Liability Management Models in Insurance and Benchmark Decomposition

Alexei A. Gaivoronski and Sergiy Krylov

Norwegian University of Science and Technology

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Contents

Contents

1. Introduction: ALM model outline

2. Approximations:

scenario trees

parametric strategies

3. Benchmark decomposition

4. Modern risk measures: VaR

5. Solution techniques

6. Architecture of software system for ALM

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Literature

Literature

  • D.R. Carino and W. Ziemba (1998)

  • G. Consigli and M.A.H. Dempster (1998)

  • A. Consiglio, F. Cocco and S. Zenios (2000)

  • J. Dupacova, M. Bertocchi and V. Moriggia (1998)

  • A. A. Gaivoronski and Petter de Lange (1999)

  • K. Hoyland and S. Wallace (1998)

  • P. Klaassen (1998)

  • H. Mausser and D. Rosen (1998)

  • J. Mulvey and H. Vladimirou (1992)

  • G. Pflug and A. Swietanowski (1998)

  • S. Zenios, M. Holmer, R. McKendall and C. Vassiadou-Zeniou (1998)

  • W. Ziemba and J. Mulvey (eds.), Worldwide Asset and Liability Management, Cambridge Univ. Press, 1998

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Asset liability management

Asset/liability management

Determine a portfolio investment strategy

over time in order to meet a sequence

of liability payments in the future

  • maximize expected utility of wealth or related objective function

  • maintain competitiveness

  • maintain adequate reserves and cash levels

  • meet regulatory requirements

Insurance company

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Motivation

Motivation

  • Increased interest for adequate risk management from the part of industry

  • Integrated ALM models are a challenge

    • dynamics and uncertainty

    • complex intertvined structure of assets/liabilities/regulatory requirement

  • Approximations to reality are inevitable

    • modeling tradeoffs between decision flexibility and representation of uncertainty

  • Two main approximation approaches:

    • scenario trees

    • parametric strategies

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Scenario tree

Scenario tree

t=0

t=1

t=2

  • Each node:

  • values of risk factors

  • decisions

Huge amount of nodes:

binomial tree with 10 random quantities

each additional time period multiplies

the number of nodes by 1000

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Scenario trees

Scenario trees

  • Some important theoretical studies and applications

  • Allow rich decision structure

    But

  • Require complex scenario generation procedures which

    • reflect dynamics of prices

    • are sound from the point of view of financial theory

    • affordable numerically

      Pflug & Swietanowski (1998),

      Hoyland & Wallace (1998)

  • Require solution of huge convex optimization problem

    Example:10 assets, one year horizon, one month time step: 1036 nodes

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Scenario trees1

Scenario trees

  • easy to represent “mainstream” events, difficult to represent events of relatively small probability

  • consequently, difficult to meaningfully utilize modern risk measures like Value-at-Risk

t=0

t=1

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Parametrization

Parametrization

  • select a class of strategies which represent asset and liability management decision as a function of state which depends on relatively small set of parameters

  • optimize the system performance with respect to these parameters

    Example: fix mix strategy: parameters - fraction of total asset value invested in a given asset

    Scenario optimization

  • Allows much richer and more adequate representation of dynamics of risk factors

  • Allows consideration of small probability events and, consequently, VaR

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Parametrization1

Parametrization

  • optimization problem is of relatively small size

    But

  • decision set is relatively restricted

  • how to elect good family of strategies is far from clear

  • optimization problem is not convex and may have local minima

  • estimation of performance necessary for optimization may be time consuming

    Tradeoff between adequate representation of uncertainty and richness of decision set

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Combined approach

Combined approach

t=0

t=1

t=2

  • scenario tree with decisions on nodes

  • for the first few periods

  • parametric strategies on later periods

A.A.Gaivoronski & P. de Lange (1999)

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Benchmark decomposition

Benchmark decomposition

  • Objectives:

    • reduce the size of the model and yet preserve expressive power

    • Permit straightforward utilization of modern risk management approaches, like VaR

  • Method: substitute the original large model with sequence of smaller models

  • Approach

    • select benchmark wealth growth process

    • choose asset portfolio from performance/risk tradeoff relative to benchmark

    • optimize liability part with respect to remaining decisions and performance/risk tradeoff

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Top level view of modeling process

Top level view of modeling process

  • Liability management

  • Debt/equity structure

  • Regulatory constraints

  • Integrated ALM performance

  • Selection of portfolio of assets

  • Portfolio risk management

  • benchmark

  • relative performance/risk tradeoff

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Model structure

Model structure

  • Benchmark

    • market index

    • wealth growth process

    • liability growth for products with guarantees

  • ALM Model components

    • liability process

    • portfolio rebalancing

    • cash flow

    • debts

    • equity

    • regulatory constraints

    • performance objective

    • decisions

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Alm model

ALM Model

time

assets

liabilities

  • Notations:

  • Portfolio rebalancing

cash inflows

debts

portfolio

relative return

bought assets

sold assets

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Alm model continued

ALM Model, continued

buying transaction costs

selling transaction costs

dividends

  • Cash flow

cash to service liabilities

external cash inflow

current debts

newly acquired debts

repaid debts

debt servicing

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Alm model continued1

ALM Model, continued

  • Debts

  • Equity

  • Regulatory constraints

    • portions of assets

    • cash reserves

    • debt restrictions

    • assets/liabilities ratio

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Alm model continued2

ALM Model, continued

  • Performance measure

  • random quantities

  • decisions

  • state variables

  • strategies

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Parametric strategies

Parametric strategies

  • Parameters

  • Parametrization

  • Problem

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Fix mix strategy

Fix mix strategy

  • LP to be solved for each time period

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Benchmark decomposition1

Benchmark decomposition

  • Benchmark

  • Portfolio optimization problem

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Risk measures

Risk measures

  • Relative regret

  • Value at Risk

  • Conditional VaR

Uryasev & Rockafellar (1999)

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Asset liability management models in insurance and benchmark decomposition

General picture

MATLAB

Data

Modeler

File

Excel,...

LP-solver

NLP solver

XPRESS(XBSL)

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


Summary

Summary

  • asset/liability management by stochastic optimization of simulation model

  • curse of dimensionality is beatable by consideration of parametrized policies

  • alternative risk measures like VaR can be incorporated in the model

  • customization of modern nonlinear optimization tools allow solution of advanced models

Universita’ degli Studi di Bergamo

Corso di dottorato di ricerca


  • Login