The numéraire portfolio in semimartingale financial models
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Publication:2463718
DOI10.1007/s00780-007-0047-3zbMath1144.91019arXiv0803.1877OpenAlexW2164288937MaRDI QIDQ2463718
Constantinos Kardaras, Ioannis Karatzas
Publication date: 16 December 2007
Published in: Finance and Stochastics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0803.1877
semimartingalenuméraire portfoliolog-utilityfree lunchpredictable characteristicssupermartingale deflator
Applications of stochastic analysis (to PDEs, etc.) (60H30) Stochastic integrals (60H05) Portfolio theory (91G10)
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Cites Work
- Unnamed Item
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- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Calcul stochastique et problèmes de martingales
- Relative arbitrage in volatility-stabilized markets
- Asymptotic optimality and asymptotic equipartiton properties of log- optimum investment
- Martingale densities for general asset prices
- The fundamental theorem of asset pricing for unbounded stochastic processes
- Hedging of contingent claims and maximum price
- A general version of the fundamental theorem of asset pricing
- Optional decompositions under constraints
- A complete explicit solution to the log-optimal portfolio problem.
- Necessary and sufficient conditions in the problem of optimal investment in incomplete markets
- The asymptotic elasticity of utility functions and optimal investment in incomplete markets
- Diversity and relative arbitrage in equity markets
- On the pricing of contingent claims under constraints
- Arbitrage possibilities in Bessel processes and their relations to local martingales
- A necessary and sufficient condition for absence of arbitrage with tame portfolios
- The existence of absolutely continuous local martingale measures
- A minimality property of the minimal martingale measure
- Martingale and Duality Methods for Utility Maximization in an Incomplete Market
- No Arbitrage and the Growth Optimal Portfolio
- Equilibrium Models With Singular Asset Prices
- Stochastic Integration with Jumps
- $\sigma$-Localization and $\sigma$-Martingales
- A BENCHMARK APPROACH TO FINANCE
- The numeraire portfolio for unbounded semimartingale
- Minimax and minimal distance martingale measures and their relationship to portfolio optimization