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David Schiess
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Dr.
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Schiess
First name
David
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david.schiess@unisg.ch
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PublicationOptimal Design of the Attribution of Pension Fund Performance to EmployeesThe article analyzes risk sharing in a defined contribution pension fund in continuous time. According to a prespecified attribution scheme, the interest rate paid on the employees' accounts is a linear function of the fund's investment performance. For each attribution scheme, the pension fund maximizes the expected utility and the employees derive utility from their savings accounts. It turns out that all Paretooptimal attribution schemes are characterized by the same optimal participation rate. We derive the total welfare gain that installs from replacing no participation with optimal participation. This welfare gain can be quantified and is substantial for reasonable parameter values.Type: journal articleJournal: The Journal of Risk and InsuranceVolume: 81Issue: 2

PublicationHow a Pensioner Should Invest, Consume, Annuitise and Bequeath( 20081022)The task of finding optimal consumption, asset allocation and the optimal annuitisation time for a pensioner leads to a combined optimal stopping and optimal control problem (COSOCP). In the nobequest case it is optimal for the pensioner to annuitse immediately or never depending on the parameters of the model. However, there is an absurd strong tendency for the annuity market which can be eliminated with the inclusion of a bequest motive. Allowing for a bequest motive and consequently, for prior life insurance and a subsistence level of bequests, makes the optimisation problem technically quite involved and normally leads to a wealthdependent annuitisation decision rule. The pensioner annuitises as soon as his wealth level falls below some threshold which exhibits a very natural parameter dependence. The main result is clearly that the essential inclusion of a bequest motive turns the very strong tendency for the annuity market into a slight tendency for the financial market. But even in the bequest case there are many realistic situations where the pensioner chooses the annuity market. This highlights the importance of longevity risk and, in combination with the intergenerational risk transfer argument discussed in Baumann and Müller (2008), it provides a legitimation for pension funds.Type: journal articleJournal: Health and Ageing Newsletter, The Geneva Association, Risk & Insurance EconomicsVolume: OctoberIssue: 19

PublicationConsumption and protfolio optimisation at the end of the lifecycle( 20080327)Consumption and portfolio optimisation during retirement has not received as much attention in financial research as optimisation prior to retirement. However, retirement planning is becoming more and more relevant for several reasons. The present paper is mainly based on Schiess (2008) and studies a pensioner deriving utility from a stream of consumption or an annuity and from bequeathing wealth to his heirs in a continuoustime framework. The task of finding the pensioner's optimal consumption, asset allocation and annuity decision rule leads to the interesting interplay of optimal control theory, optimal stopping theory and mortality issues or, technically speaking, to a combined optimal stopping and optimal control problem (COSOCP). Stabile (2006) solved this problem in an allornothing framework assuming exponential mortality and power utility functions. In this paper we present the extensions of Schiess (2008) to the model of Stabile (2006):The essential inclusion of a bequest motive, the additional study of the economically interesting range of relative risk aversion levels greater than one and a new solution method for the COSOCP via duality arguments. For identical risk aversion levels Stabile (2006) finds that the pensioner either annuitises immediately or never which means that COSOCP reduces to a trivial or to a pure optimal control problem. In contrast to this, the annuitisation decision rule can become wealthdependent in our more general model and consequently, a real COSOCP has to be dealt with. The main result is that longevity risk matters very much (quite attractive annuity market) even if we allow for a bequest motive.Type: conference paper

PublicationConsumption and Portfolio Optimisation at the End of the LifeCycleThe thesis' focus is on the consumption/portfolio optimisation and the optimal annuitisation decision of a pensioner in a continuous time setting. Technically, this involves solving a combined optimal stopping and optimal control problem (COSOCP). The retiree faces the crucial question of how much to consume and how much to invest in the risky asset (financial market risk). This creates the optimal control aspect of the COSOCP. Any prior decisions on annuities and life insurance are taken as given. The second source of uncertainty is the pensioner's longevity risk, which is why we include an annuity market. The pensioner has to find the optimal time to annuitise his wealth. This constitutes the optimal stopping aspect of the COSOCP. Stabile (2006) provides an appropriate model to solve the mentioned COSOCP. Among other things we mainly contribute a new solution method for this COSOCP via duality arguments, the study of the economically interesting range of relative risk aversions greater than one and the essential inclusion of a bequest motive (annuitisation is in conflict with a potential bequest motive). The first part of the thesis lays down the necessary theoretical foundations for the COSOCP. We model the utility, which the pensioner derives from a stream of consumption or an annuity, and define his utility from bequests. Later, we will specify the pensioner's preferences to power utility and subsistence level utility functions. Afterwards, we discuss the three major ingredients for solving the pensioner's COSOCP: Optimal control theory, optimal stopping theory and mortality concepts. The second part of the thesis exploits the theoretical foundations of the first part. We only solve a pure optimal control problem under the GompertzMakeham mortality law. We are able to derive interesting comparisons; however, this problem is already quite involved and helps us to understand why we have to employ the less complicated exponential mortality law in a real COSOCP. The exponential mortality law has the great advantage of increased mathematical tractability. We use it to solve two different models. In the first model we impose that the relative risk aversion is the same for all utility functions: Utility from consumption, annuity and bequests. Most often the annuitisation decision is then of the nowornever type: Depending on the model parameters, annuitisation either occurs immediately or never (reduction to a pure optimal control problem). We solve both cases and show how the annuitisation decision is influenced by the model parameters. Finally, the second model provides an extension to the first one by allowing for a higher relative risk aversion in the postannuitisation phase. This last model leads to a real COSOCP in most cases. After exploiting some duality arguments, we arrive at a slightly nonlinear ordinary differential equation for the dual value function. While the nobequest case allows a quasianalytical solution, the bequest case has to be solved numerically. We give general characteristics of the optimal consumption and investment rule and numerically show how they depend on the parameters. Finally, we simulate the optimal annuitisation rule.Type: doctoral thesis

PublicationAssetLiabilitySoftware für PensionskassenType: newspaper articleJournal: AWP Soziale SicherheitIssue: Sonderbeilage

PublicationDer Einfluss des technischen ZinssatzesType: newspaper articleJournal: Schweizer Personalvorsorge : Zeitschrift für alle Fragen der beruflichen Vorsorge und der SozialversicherungIssue: 02

Publication

PublicationAsset Allocation, Longevity Risk, Annuitisation and Bequests( 20090414)Consumption and portfolio optimisation during retirement has not received as much attention in financial research as optimisation prior to retirement. However, retirement planning is becoming more and more relevant for several reasons. The present paper is mainly based on Schiess (2008) and studies a pensioner deriving utility from a stream of consumption or an annuity and from bequeathing wealth to his heirs in a continuoustime framework. The task of finding the pensioner's optimal consumption, asset allocation and annuity decision rule leads to the interesting interplay of optimal control theory, optimal stopping theory and mortality issues or, technically speaking, to a combined optimal stopping and optimal control problem (COSOCP). Stabile (2006) solved this problem in an allornothing framework assuming exponential mortality and power utility functions. In this paper we present the extensions of Schiess (2008) to the model of Stabile (2006):The essential inclusion of a bequest motive, the additional study of the economically interesting range of relative risk aversion levels greater than one and a new solution method for the COSOCP via duality arguments. For identical risk aversion levels Stabile (2006) finds that the pensioner either annuitises immediately or never which means that COSOCP reduces to a trivial or to a pure optimal control problem. In contrast to this, the annuitisation decision rule can become wealthdependent in our more general model and consequently, a real COSOCP has to be dealt with. The main result is that longevity risk matters very much (quite attractive annuity market) even if we allow for a bequest motive.Type: presentation

PublicationAsset Allocation, Longevity Risk, Annuitisation and Bequests( 20080327)Consumption and portfolio optimisation during retirement has not received as much attention in financial research as optimisation prior to retirement. However, retirement planning is becoming more and more relevant for several reasons. The present paper is mainly based on Schiess (2008) and studies a pensioner deriving utility from a stream of consumption or an annuity and from bequeathing wealth to his heirs in a continuoustime framework. The task of finding the pensioner's optimal consumption, asset allocation and annuity decision rule leads to the interesting interplay of optimal control theory, optimal stopping theory and mortality issues or, technically speaking, to a combined optimal stopping and optimal control problem (COSOCP). Stabile (2006) solved this problem in an allornothing framework assuming exponential mortality and power utility functions. In this paper we present the extensions of Schiess (2008) to the model of Stabile (2006):The essential inclusion of a bequest motive, the additional study of the economically interesting range of relative risk aversion levels greater than one and a new solution method for the COSOCP via duality arguments. For identical risk aversion levels Stabile (2006) finds that the pensioner either annuitises immediately or never which means that COSOCP reduces to a trivial or to a pure optimal control problem. In contrast to this, the annuitisation decision rule can become wealthdependent in our more general model and consequently, a real COSOCP has to be dealt with. The main result is that longevity risk matters very much (quite attractive annuity market) even if we allow for a bequest motive.Type: presentation

PublicationOptimal Design of the Attribution of Pension Fund Peformance to EmployeesThe paper analyses a definedcontribution pension fund in continuous time. According to a prespecified attribution scheme the interest rate paid on the employees' accounts is a linear function of the fund's investment performance. An attribution scheme consists of a articipation rate and an intercept. For each attribution scheme the pension fund maximises the expected utility of the funding ratio at the end of a planning horizon and the employees derive utility from their savings accounts at the time they exit the plan. Solving the optimisation problem of the pension fund leads to constant optimal investment strategies. For the pension fund and the employees, respectively, indirect utility functions can be derived on the set of attributions. It turns out that all Paretooptimal attribution schemes are characterised by the same optimal participation rate. As a main result, we derive the total welfare gain  measured by the increase in appropriate certainty equivalents of the pension fund and the employees, respectively  that installs from replacing no participation with optimal participation. For reasonable parameter values a substantial increase in the riskadjusted rate of return on employees' accounts can be achieved if the welfare gain is fully attributed to the employees.