The numeraire portfolio for unbounded semimartingales

Becherer, Dirk

doi:10.1007/pl00013535

Cited by 121 publications

(156 citation statements)

References 19 publications

Supporting

Mentioning

151

Contrasting

Unclassified

Order By: Relevance

“…Suppose that there exists some neutral derivative price process S 2 for H. We will show in Step 4 that this leads to a contradiction. By absence of arbitrage S Since S 1 is the wealth process of an optimal strategy, both S 2 /S 1 and −S 2 /S 1 are supermartingales by [1], Proposition 4.3. From S…”

Section: )mentioning

confidence: 99%

On utility-based derivative pricing with and without intermediate trades

Kallsen¹,

Kühn²

2006

Statistics &Amp; Decisions

View full text Add to dashboard Cite

The neutral valuation approach for contingent claims in incomplete markets is based on the assumption that investors are identical utility maximizers and that derivative supply and demand are balanced. It is closely related to (marginal) utility-based pricing in the sense of Hugonnier et al. (2005), where however only buy-and-hold investments in the derivative are possible.This paper contains four results: Firstly, it is shown that neutral derivative prices exist in discrete-time markets with finite time horizon. They are characterized as martingales relative to certain finitely additive set functions. Secondly, it may happen that not any static utility-based derivative price can be extended to yield a neutral price process. Thirdly, neutral derivative prices may not exist in continuous-time markets. Finally, we consider the situation of finite utility on the whole real line.

show abstract

Section: )mentioning

confidence: 99%

On utility-based derivative pricing with and without intermediate trades

Kallsen¹,

Kühn²

2006

Statistics &Amp; Decisions

View full text Add to dashboard Cite

show abstract

“…Because of the additively separable form of the value function, the optimal portfolio is always myopic. It is known as the "growth optimal portfolio" and has been extensively studied in general market settings (see, for example, [6] and [50]). The associated optimal wealth is the so-called "numeraire portfolio".…”

Section: The Cara Crra and Logarithmic Casesmentioning

confidence: 99%

“…As the theorem below shows, the optimal processes can be calculated in closed form. 6 One may alternatively represent h as h (x; t) = R +1 0 e yx 1 2 y 2 t (dy) with (dy) = (dy) y : Note that 2 B + (R) : Such a representation was used in [5].…”

Section: Proposition 6 I) Let 2 Bmentioning

confidence: 99%

Optimal asset allocation in a stochastic factor model – an overview and open problems

Albrecher¹,

Runggaldier²,

Schachermayer³

2009

Advanced Financial Modelling

View full text Add to dashboard Cite

This paper provides an overview of the optimal investment problem in a market in which the dynamics of the risky security are a¤ected by a correlated stochastic factor. The performance of investment strategies is measured using two criteria. The …rst criterion is the traditional one, formulated in terms of expected utility from terminal wealth while the second is based on the recently developed forward investment performance approach.

show abstract

“…The basic assumption of the current paper is concerned with the existence of the NP, which has been studied in many papers including Long (1990), BajeuxBesnainou and Portait (1997), Becherer (2001), Platen (2002), Bühlmann and Platen (2003), Platen (2006), Platen and Heath (2006), Karatzas and Kardaras (2007) and Kardaras and Platen (2008). For the NP its current benchmarked value is greater than or equal to its future expected benchmarked values.…”

Section: Introductionmentioning

confidence: 99%

Approximating the numéraire portfolio by naive diversification

Platen

Rendek

2011

J Asset Manag

View full text Add to dashboard Cite

Abstract. Estimation theory has shown, due to the limited estimation window available for real asset data, the sample based Markowitz mean-variance approach produces unreliable weights which fluctuate substantially over time. This paper proposes an alternate approach to portfolio optimization, being the use of naive diversification to approximate the numéraire portfolio. The numéraire portfolio is the strictly positive portfolio that, when used as benchmark, makes all benchmarked nonnegative portfolios either mean decreasing or trendless. Furthermore, it maximizes expected logarithmic utility and outperforms any other strictly positive portfolio in the long run. The paper proves for a well-securitized market that the naive equal value weighted portfolio converges to the numéraire portfolio when the number of constituents tends to infinity. This result is model independent and, therefore, very robust. The systematic construction of diversified stock indices by naive diversification from real data is demonstrated. Even when taking transaction costs into account, these indices significantly outperform the corresponding market capitalization weighted indices in the long run, indicating empirically their asymptotic proximity to the numéraire portfolio. Finally, in time of financial crisis, a large equi-weighted fund carrying the investments of major pension funds and insurance companies would provide important liquidity. It would not only dampen the drawdown of a crisis but would also moderate the excesses of an asset price bubble.

show abstract

The numeraire portfolio for unbounded semimartingales

Cited by 121 publications

References 19 publications

On utility-based derivative pricing with and without intermediate trades

On utility-based derivative pricing with and without intermediate trades

Optimal asset allocation in a stochastic factor model – an overview and open problems

Approximating the numéraire portfolio by naive diversification

Contact Info

Product

Resources

About