Correction: Pfeifer, D.; Ragulina, O. Adaptive Bernstein Copulas and Risk Management. Mathematics 2020, 8, 2221

Dietmar Pfeifer; Olena Ragulina

doi:10.3390/math9141646

and

¹

Institute of Mathematics, Carl von Ossietzky Universität Oldenburg, D-26111 Oldenburg, Germany

²

Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska Str. 64, 01601 Kyiv, Ukraine

^*

Author to whom correspondence should be addressed.

Mathematics2021, 9(14), 1646;https://doi.org/10.3390/math9141646

Version Notes

Order Reprints

The authors wish to make the following corrections to this paper [1]:

1.

On Page 9, relation (17) is given by

r_{i j}^{+} : = r_{i, ⌈\frac{j}{M}⌉} (⌈\frac{j}{M}⌉ M + 1 - j), i = 1, \dots, d, j = 1, \dots, M n .

(17)

This should read

r_{i j}^{+} : = r_{i, ⌈\frac{j}{M}⌉} M + (⌈\frac{j}{M}⌉ - 1) M + 1 - j, i = 1, \dots, d, j = 1, \dots, M n .

(17)

2.

On Page 9, Table 5 is given by

Table 5. Ranks

r_{i j}

and probabilities

p (r_{1}, r_{2})

in Example 4.

This should read

Table 5. Ranks

r_{i j}

and probabilities

p (r_{1}, r_{2})

in Example 4.

Table 5. Ranks

r_{i j}

and probabilities

p (r_{1}, r_{2})

in Example 4.

$j ∖ i$	1	2	$p (r_{1}, r_{2})$
1	1	3	0.2
2	2	4	0.2
3	3	1	0.2
4	4	2	0.2
5	5	5	0.2

The authors would like to apologize for any inconvenience caused to the readers by these changes, and to thank B.Sc. Lennard Foraita for pointing out the error in relation (17).

The authors apologize for any inconvenience caused and state that the scientific conclusions are unaffected. The original article has been updated.

Conflicts of Interest

The authors declare no conflict of interest.

References

Pfeifer, D.; Ragulina, O. Adaptive Bernstein copulas and risk management. Mathematics 2020, 8, 2221. [Google Scholar] [CrossRef]

Table 5. Ranks

r_{i j}

and probabilities

p (r_{1}, r_{2})

in Example 4.

Table 5. Ranks

r_{i j}

and probabilities

p (r_{1}, r_{2})

in Example 4.

$j ∖ i$	1	2	$p (r_{1}, r_{2})$
1	1	2	0.2
2	2	4	0.2
3	3	1	0.2
4	4	2	0.2
5	5	5	0.2

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Correction: Pfeifer, D.; Ragulina, O. Adaptive Bernstein Copulas and Risk Management. Mathematics 2020, 8, 2221

Conflicts of Interest

References

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