Continuous-time (Ross-type) portfolio separation, (almost) without Itô calculus

References

• R. Agnew, Counter-examples to an assertion concerning the normal distribution and a new stochastic price fluctuation model, Rev. Econ. Stud. 38 (1971), pp. 381–383.
   Web of Science ®Google Scholar
• D. Applebaum, Lévy Processes and Stochastic Calculus, Vol. 93, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 2004.
   Google Scholar
• G.B. Asheim, Intergenerational equity, Ann. Rev. Econ. 2 (2010), pp. 197–222.
   Web of Science ®Google Scholar
• G.B. Asheim, and S. Zuber, A complete and strongly anonymous leximin relation on infinite streams, Soc. Choice Welfare 41 (2013), pp. 819–834.
   Web of Science ®Google Scholar
• L. Belkacem, J.L. Véhel, and C. Walter, CAPM, risk and portfolio selection in “α-stable markets”, Fractals 08 (2000), pp. 99–115.
   Web of Science ®Google Scholar
• K. Borch, A note on uncertainty and indifference curves, Rev. Econ. Stud. 36 (1969), pp. 1–4.
   Web of Science ®Google Scholar
• B.O. Bradley and M.S. Taqqu, Financial risk and heavy tails, in Handbook of Heavy Tailed Distributions in Finance, S.T. Rachev,ed., Elsevier, Amsterdam, 2003, pp. 35–103.
   Google Scholar
• S. Cambanis, S. Huang, and G. Simons, On the theory of elliptically contoured distributions, J. Multivariate Anal. 11 (1981), pp. 368–385.
   Web of Science ®Google Scholar
• D. Cass, and J.E. Stiglitz, The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds, J. Econ. Theory 2 (1970), pp. 122–160.
   Web of Science ®Google Scholar
• G. Chamberlain, A characterization of the distributions that imply mean–variance utility functions, J. Econ. Theory 29 (1983), pp. 185–201.
   Web of Science ®Google Scholar
• B. de Finetti, Il problema dei “pieni” [The problem of full-risk insurances], Giorn. Ist. Ital. Attuari 11 (1940), pp. 1–88.
   Google Scholar
• N. Dokuchaev, Mutual fund theorem for continuous time markets with random coefficients, Theory Decis. 76 (2014), pp. 179–199.
   Web of Science ®Google Scholar
• R.M. Dudley, Wiener functionals as Itô integrals, Ann. Probab. 5 (1977), pp. 140–141.
   Web of Science ®Google Scholar
• E.F. Fama, Portfolio analysis in a stable Paretian market, Manage. Sci. 11 (1965), pp. 404–419.
   Web of Science ®Google Scholar
• E.F. Fama, Risk, return, and equilibrium, J. Political Econ. 79 (1971), pp. 30–55.
   Web of Science ®Google Scholar
• M.S. Feldstein, Mean-variance analysis in the theory of liquidity preference and portfolio selection, Rev. Econ. Stud 36 (1969), pp. 5–12.
   Web of Science ®Google Scholar
• N.C. Framstad, Coherent portfolio separation–inherent systemic risk?, Int. J. Theor. Appl. Finance 7 (2004), pp. 909–917.
   Google Scholar
• N.C. Framstad, On Portfolio Separation in the Merton Problem with Bankruptcy or Default, in Proceedings of the International Conference on Stochastic Analysis and Applications, Sergio Albeverio, Anne Boutet de Monvel, and Habib Ouerdiane, eds., Kluwer Academic Publishers, Dordrecht, 2004, pp. 249–265.
   Google Scholar
• N.C. Framstad, Portfolio separation properties of the skew-elliptical distributions, with generalizations, Statist. Probab. Lett. 81 (2011), pp. 1862–1866.
   Web of Science ®Google Scholar
• N.C. Framstad, Portfolio theory for α-symmetric and pseudo-isotropic distributions: k-fund separation and the CAPM, J. Probab. Stat. 2015 (2015), 235452, 11 p.
   Google Scholar
• B. Gamrowski and S. Rachev, A testable version of the Pareto-stable CAPM, Math. Comput. Model. 29 (1999), pp. 61–81.
   Google Scholar
• E.D. Giorgi, T. Hens, and J. Mayer, A note on reward-risk portfolio selection and two-fund separation, Finance Res. Lett. 8 (2011), pp. 52–58.
   Web of Science ®Google Scholar
• P. Guasoni and S. Robertson, Static fund separation of long-term investments, Math. Finance. 25 (2015), pp. 789–826.
   Web of Science ®Google Scholar
• A.K. Gupta, T.T. Nguyen, and W.B. Zeng, Conditions for stability of laws with all projections stable, Sankhyā: Indian J. Stat., Ser. A (1961–2002) 56 (1994), pp. 438–443.
   Google Scholar
• A.K. Gupta, T. Varga, and T. Bodnar, Elliptically Contoured Models in Statistics and Portfolio Theory 2nd ed., Springer, New York, 2013.
   Google Scholar
• P. Hall, A Comedy of Errors: The canonical form for a stable characteristic function, Bull. London Math. Soc. 13 (1981), pp. 23–27.
   Web of Science ®Google Scholar
• X.D. He, and X.Y. Zhou, Portfolio choice via quantiles, Math. Finance 21 (2011), pp. 203–231.
   Web of Science ®Google Scholar
• A.W. Janicki, I. Popova, P.H. Ritchken, and P.H. Ritchken, Option pricing bounds in an α-stable security market, Comm. Stat. Stoch. Models 13 (1997), pp. 817–839.
   Google Scholar
• T. Kamae, and U. Krengel, Stochastic partial ordering, Ann. Probab. 6 (1979), pp. 1044–1049.
   Web of Science ®Google Scholar
• T. Kamae, U. Krengel, and G.L. O’Brien, Stochastic inequalities on partially ordered spaces, Ann. Probab. 5 (1977), pp. 899–912.
   Web of Science ®Google Scholar
• A. Khanna and M. Kulldorff, A generalization of the mutual fund theorem, Finance Stoch. 3 (1999), pp. 167–185.
   Google Scholar
• B.B. Mandelbrot, Fractals and Scaling in Finance, Springer-Verlag, New York, 1997.
   Google Scholar
• D.J. Marcus, Nonstable laws with all projections stable, Z. Wahrsch. Verw. Gebiete 64 (1983), pp. 139–156.
   Web of Science ®Google Scholar
• H. Markowitz, Portfolio selection, J. Finance 7 (1952), pp. 77–91.
   Web of Science ®Google Scholar
• H. Markowitz, de Finetti scoops Markowitz, J. Invest. Manage. 4 (2006), pp. 3–18.
   Google Scholar
• J.H. McCulloch, Measuring tail thickness to estimate the stable index α: A critique, J. Bus. Econ. Stat. 15 (1997), pp. 74–81.
   Web of Science ®Google Scholar
• J.H. McCulloch, Skew-stable investment opportunity set, 1999. Available at http://www.econ.ohio-state.edu/jhm/ios.html.
   Google Scholar
• R.C. Merton, Optimum consumption and portfolio rules in a continuous-time model, J. Econ. Theory 3 (1971), pp. 373–413.
   Web of Science ®Google Scholar
• R.C. Merton, Erratum: “Optimum consumption and portfolio rules in a continuous-time model”, J. Econ. Theory. 3 (1971), pp. 373–413; J. Econ. Theory, 6 (1973), pp. 213--214.
   Web of Science ®Google Scholar
• R.C. Merton, Continuous-time Finance, Revised ed., Blackwell, Oxford, 1992.
   Google Scholar
• J.K. Misiewicz, Infinite divisibility of sub-stable processes. I. Geometry of sub-spaces of Lα-space, Stoch. Process. Appl. 56 (1995), pp. 101–116.
   Web of Science ®Google Scholar
• J.K. Misiewicz, Infinite divisibility of sub-stable processes. II. Logarithm of probability measure, J. Math. Sci. 81 (1996), pp. 2970–2979.
   Google Scholar
• S. Mittnik and S.T. Rachev, Stable Paretian Models in Finance, Wiley, New York, 2000.
   Google Scholar
• J.P. Nolan, Stable distributions -- Models for heavy tailed data, book in progress, 2014. Available at http://academic2.american.edu/~jpnolan.
   Google Scholar
• B. Øksendal, Stochastic Differential Equations. An Introduction with Applications. 5th ed., Universitext, Springer-Verlag, Berlin, 1998.
   Google Scholar
• S. Ortobelli, I. Huber, S.T. Rachev, and E.S. Schwartz, Portfolio choice theory with non-Gaussian distributed returns, in Handbook of Heavy Tailed Distributions in Finance, S.T. Rachev,ed., Elsevier, Amsterdam, 2003, pp. 547–594.
   Google Scholar
• S. Ortobelli, I. Huber, and E. Schwartz, Portfolio selection with stable distributed returns, Math. Methods Oper. Res. 55 (2002), pp. 265–300.
   Web of Science ®Google Scholar
• L.P. Østerdal, The mass transfer approach to multivariate discrete first order stochastic dominance: Direct proof and implications, J. Math. Econ. 46 (2010), pp. 1222–1228.
   Web of Science ®Google Scholar
• J. Owen, and R. Rabinovitch, On the class of elliptical distributions and their applications to the theory of portfolio choice, J. Finance 38 (1983), pp. 745–752.
   Web of Science ®Google Scholar
• F. Pressacco, and P. Serafini, The origins of the mean-variance approach in finance: revisiting de Finetti 65 years later, Decis. Econ. Finance 30 (2007), pp. 19–49.
   Google Scholar
• P.E. Protter, Stochastic Integration and Differential Equations, Stochastic Modelling and Applied Probability 2nd ed., Vol. 21, Springer-Verlag, Berlin, 2005. Version 2.1, Corrected third printing.
   Google Scholar
• S.T. Rachev,ed. Handbook of Heavy Tailed Distributions in Finance. Elsevier, Amsterdam, 2003.
   Google Scholar
• S.A. Ross, Mutual fund separation in financial theory -– The separating distributions, J. Econ. Theory 17 (1978), pp. 254–286.
   Web of Science ®Google Scholar
• A.D. Roy, Safety first and the holding of assets, Econometrica 20 (1952), pp. 431–449.
   Web of Science ®Google Scholar
• G. Samorodnitsky and M.S. Taqqu, Stable non-Gaussian Random Processes. Stochastic Models with Infinite Variance, Chapman & Hall, New York, 1994.
   Google Scholar
• P.A. Samuelson, Efficient portfolio selection for Pareto-Lévy investments, J. Financ. Quant. Anal. 2 (1967), pp. 107–122.
   Web of Science ®Google Scholar
• P.A. Samuelson, General proof that diversification pays, J. Financ. Quant. Anal. 2 (1967), pp. 1–13.
   Web of Science ®Google Scholar
• W. Schachermayer, M. Sîrbu, and E. Taflin, In which financial markets do mutual fund theorems hold true?, Finance Stoch. 13 (2009), pp. 49–77.
   Web of Science ®Google Scholar
• I.J. Schoenberg, Metric spaces and completely monotone functions, Ann. Math. (2). 39 (1938), pp. 811–841.
   Google Scholar
• I.J. Schoenberg, Metric spaces and positive definite functions, Trans. Am. Math. Soc. 44 (1938), pp. 522–536.
   Google Scholar
• S.P. Sethi and M. Taksar, A note on R. C. Merton’s: “Optimum consumption and portfolio rules in a continuous-time model”, J. Econ. Theory. 46 (1988), pp. 395–401.
   Web of Science ®Google Scholar
• J. Tobin, Liquidity preference as behavior toward risk, Rev. Econ. Stud. 25 (1958), pp. 65–86.
   Web of Science ®Google Scholar
• L.Barone, Bruno de Finetti and the case of the critical line’s last segment, Paper prepared for the "Bruno de Finetti Centenary Conference”, Accademia dei Lincei, Rome, 2006. Available at http://www.brunodefinetti.it/Bibliografia/Last\%20Segment.pdf.
   Google Scholar
• L.Barone, Bruno de Finetti, the problem of “full-risk insurances”, J. Invest. Manage. 4 (2006), pp. 19–43.
   Google Scholar