Robust portfolio selection under exponential preferences

Zawisza, Dariusz

doi:10.4064/am37-2-6

Cited by 8 publications

(12 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For literature review about finite horizon max-min problems we refer to Bordigoni et al [3], Hernández and Schied [8], Mataramvura and Øksendal [12], Øksendal and Sulem [15], Trybu la and Zawisza [17] and Zawisza [19].…”

Section: Introductionmentioning

confidence: 99%

Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences—Stochastic Factor Case

Trybuła

Zawisza

2019

Mathematics of OR

Self Cite

View full text Add to dashboard Cite

This is a follow up of our previous paper -Trybu la and Zawisza [17], where we considered a modification of a monotone mean-variance functional in continuous time in stochastic factor model. In this article we address the problem of optimizing the mentioned functional in a market with a stochastic interest rate. We formulate it as a stochastic differential game problem and use Hamilton-Jacobi-Bellman-Isaacs equations to derive the optimal investment strategy and the value function.2010 Mathematics Subject Classification. 91G10; 91G30; 91A15; 93E20. Key words and phrases. Stochastic interest rate, stochastic control, stochastic games. J π,η (x, y, r, t) over a class of admissible strategies A x,y,r,t .As usually, the problem (2.3) might be considered as a zero-sum stochastic differential game problem. We are looking for a saddle point (π * , η * ) ∈ A x,y,r,t × M and a value function V (x, y, r, t) such that J π * ,η (x, y, r, t) J π * ,η * (x, y, r, t) J π,η * (x, y, r, t) and V (x, y, r, t) = J π * ,η * (x, y, r, t).

show abstract

Section: Introductionmentioning

confidence: 99%

Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences—Stochastic Factor Case

Trybuła

Zawisza

2019

Mathematics of OR

Self Cite

View full text Add to dashboard Cite

show abstract

“…We now formulate a Verification Theorem. The proof of this theorem is similar to the proof of theorems from[18] [31] [32][37]. For the completeness of this analysis we briefly state the theorem.…”

mentioning

confidence: 80%

Robust Portfolio Allocation for a Bank under Inflation

Perera¹

2018

TEL

View full text Add to dashboard Cite

In this study, we develop a robust portfolio allocation model for a bank in an incomplete market with inflation (a non-tradeable stochastic factor). The optimality criterion of the investments is established on a functional via a modified version of the monotone mean-variance preferences. An increase in anticipated inflation will increase the interest rate, while reducing the expected net stream of dollar receipts in the loan portfolio. Eventually whilst existing loans mature and are renegotiated (at the higher interest rate), the interest rate is earned by the bank on existing loans are locked up. Under such explicit risk aggregation paradigm, we formulate this problem as a stochastic differential game (SDG) and apply the Hamilton-Jacobi-Bellman-Isaacs (HJBI)-equation to derive the optimal investment strategy. We discuss the dynamics of myopic optimal portfolio and the intertemporal hedging demand portfolio of the optimal portfolio holdings. We describe the dynamics of the total capital ratio under Basel III regulations. Finally, we show that our solution coincides with the solution to classical Markowitz optimization problem with risk aversion coefficient depends on stochastic factor. Our results confirm that the banker's optimal holdings and the trade-off between holding a myopically optimal portfolio and intertemporal hedging demand are determined by the derivatives of marginal utility with respect to the state variable.

show abstract

“…Finally, by substituting (26) and (27) back in (34) yields to the partial differential equation (30) According to our program, it remains to justify that the control processes (26), (27), (28) and (29) we derived in Theorem 4.1 are indeed optimal. In this direction, we modify a similar result of Mataramwura and Øksendal [26] and Zawisza [40], and get the following result. Before proceeding any further, we defineS :…”

Section: The Hamilton-jacobi-bellman-isaacs Equation and General Solumentioning

confidence: 97%

“…This method has been heavily used in the relative literature with success by many authors and within a wide range of applications, see e.g. Baltas and Yannacopoulos [5], Branger et.al [8], Cairns [14], Cont [15], Flor and Larsen [18], Korn [22], Rieder and Wopperer [34], Zawisza [40,41] and references therein.…”

mentioning

confidence: 99%

Robust portfolio decisions for financial institutions

Baltas¹,

Xepapadeas²,

Yannacopoulos³

2018

Journal of Dynamics &Amp; Games

View full text Add to dashboard Cite

The present paper aims to study a robust-entropic optimal control problem arising in the management of financial institutions. More precisely, we consider an economic agent who manages the portfolio of a financial firm. The manager has the possibility to invest part of the firm's wealth in a classical Black-Scholes type financial market, and also, as the firm is exposed to a stochastic cash flow of liabilities, to proportionally transfer part of its liabilities to a third party as a means of reducing risk. However, model uncertainty aspects are introduced as the manager does not fully trust the model she faces, hence she decides to make her decision robust. By employing robust control and dynamic programming techniques, we provide closed form solutions for the cases of the (i) logarithmic; (ii) exponential and (iii) power utility functions. Moreover, we provide a detailed study of the limiting behavior, of the associated stochastic differential game at hand, which, in a special case, leads to break down of the solution of the resulting Hamilton-Jacobi-Bellman-Isaacs equation. Finally, we present a detailed numerical study that elucidates the effect of robustness on the optimal decisions of both players.

show abstract

Robust portfolio selection under exponential preferences

Cited by 8 publications

References 16 publications

Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences—Stochastic Factor Case

Continuous-Time Portfolio Choice Under Monotone Mean-Variance Preferences—Stochastic Factor Case

Robust Portfolio Allocation for a Bank under Inflation

Robust portfolio decisions for financial institutions

Contact Info

Product

Resources

About