Goll, T. and Kallsen, J. (2000) Optimal portfolios for logarithmic utility. Stoch. Proc. Appl. 89, 31-48.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... and Shephard [3] Recently, many authors have studied portfolio optimization problems with asset dynamics going beyond the classical geometric Brownian motion (or the Samuelson model) We would like to mention Bank and Riedel [2] Benth, Karlsen and Reikvam [5, 6, 7, 8] Goll and Kallsen [14] and Kallsen [21] which model the risky asset as an exponential of a L evy process, and Framstad, ksendal and Sulem [17, 18] using a geometric stochastic di erential equation driven by a L evy process as stock price model. All these references are based on asset dynamics which do not take ....

Th. Goll and J. Kallsen, Optimal portfolios for logarithmic utility, Stochastic Process. Appl. 89(1) (2000), 31-48.

.... ij L j ) 1 ij L j in formula (2.7) whereas the Brownian component remains the same as in ( L) i : The following Lemma describes the relation between the characteristic triplets of a L evy process and its stochastic exponential, which we need in the sequel. Lemma 2.2. Goll and Kallsen [16]) If L is a real valued L evy process with characteristic triplet (a; then also b L de ned by e = E( b L) is a L evy process with characteristic triplet (ba; b ; b ) given by ba a = 1 1)1 f(je x 1j 1g x1 fjxj 1g b = 2.8) b ( fx 2 Rje 1 2 g) for any ....

Goll, T. and Kallsen, J. (2000) Optimal portfolios for logarithmic utility. Stoch. Proc. Appl. 89, 31-48.

....i is such that ij L j = E( b L i ) i = 1; d ; where E denotes the stochastic exponential of a process. We shall use the following lemma which relates the characteristic triplet of an exponential L evy process and its stochastic exponential in . Lemma 5.15. Goll and Kallsen [43]) If L is a real valued L evy process with characteristic triplet (a; then also b L de ned by = E( b L) is a L evy process with characteristic triplet (ba; b ; b ) given by ba a = 1 1)1 f(je 1j 1g x1 fjxj 1g b = b ( fx 2 : e 1 2 g) for any Borel set . ....

Goll, T. and Kallsen, J. (2000) Optimal portfolios for logarithmic utility. Stoch. Proc. Appl. 89, 31-48.

....setting may depend on t 2 [0; T ] and 2 Omega in an F t measurable way, satisfy the reasonable elasticity condition in a uniform way. Results related to the duality theory of utility maximization and notably to the dual optimizer b Q 2 M e (S) were obtained in [F 00] K 00] XY 00] 31 [GK 00] GR 00] and [BF 00] Utility maximisation under transaction costs was investigated, e.g. in [HN 89] CK 96] CW 00] and [DPT 00] in the latter two papers the phenomenon arising in Theorem 3.4 i of crucial importance: for the dual optimizer one has to perform a similar enlargement as the ....

T. Goll, J. Kallsen, (2000), Optimal portfolios for logarithmic utility. Stochastic Processes and Their Applications, Vol. 89, pp. 31--48.

....also Kallsen (1998) It is usually quite hard to compute optimal strategies explicitly unless the market is of a certain simple structure or the logarithm is chosen as utility function. We refer to Hakansson (1971) Merton (1971) Aase (1984) Karatzas et al. 1991) Cvitani c Karatzas (1992) Goll Kallsen (1999) for the latter case. In this paper, time homogeneous models are considered for power, logarithmic, and exponential utility functions. We suppose that logarithmic securities prices follow a process with independent, stationary increments. Our problem has been solved by Merton (1969) for continuous ....

....2. 2 L( b S) and t b S t = 0 b S 0 R t 0 s d b S s for any t 2 R . Note that it is not necessary to assume that S 0 is predictable as is for simplicity often done in the literature. For the definition of multidimensional integrals cf. Jacod (1980) PROOF. cf. Goll Kallsen (1999) We call a trading strategy 2 L( b S) with 0 = 0 self financing if t b S t = R t 0 s d b S s for any t 2 R . A self financing strategy belongs to the set S of all admissible strategies if its discounted gains process R Delta 0 t b S t is bounded from below. Fix a ....

[Article contains additional citation context not shown here]

Goll, T. and J. Kallsen (1999). Optimal portfolios for logarithmic utility. Preprint.

No context found.

Goll, T. and Kallsen, J. (2000) Optimal portfolios for logarithmic utility. Stoch. Proc. Appl. 89, 31-48.

No context found.

Goll, T. and Kallsen, J. (2000) Optimal portfolios for logarithmic utility. Stoch. Proc. Appl. 89, 31-48.

No context found.

T. Goll, J. Kallsen, (2000), Optimal portfolios for logarithmic utility. Stochastic Processes and Their Applications, Vol. 89, pp. 31--48.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC